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COAiPLIhdElUTS 

AMERICAN  BOOK  CO 

A.  P.  GUNN.  Crea'l  Ao'i, 
PIN  E  &  BATTERY 

■""^    FRANCISCO 


THE         (^.;::],AV-'-=- 

ARITHMETIC  PRIMER 


AN   INDEPENDENT   NUMBER   BOOK 

DESIGNED    TO    PBECEDE   ANY 

SERIES  OF  ARITHMETICS 


BY 

FRANK  H.  HALL 

ATTTHOR  OP  "THE  ARITHMETIC    READERS,"  "THE  ARITHMETIC  OF  THE  FARM  AND 

■WORK-SHOP,"   "THE   WERNER  ARITHMETICS,"    "THE  HALL   ARITHMETICS,' 

AND  A  MONOGRAPH  ENTITLED,  "ARITHMETIC:  HOW  TO  TEACH  IT." 


NEW  YORK  .-.  CINCINNATI .-.  CHICAGO 
AMERICAN    BOOK    COMPANY 


HALL'S  MATHEMATICAL  SERIES 


THE    WERNEK    ARITHMETICS 

A  Three-Book  Course  for  Graded  Schools 

Book  I.  For  third  and  fourth  grades,  cloth,  256  pages,  40c. 
Book  II.  For  fifth  and  sixth  grades,  cloth,  288  pages,  40c. 
Book  III.  For  seventh  and  eighth  grades,  cloth,  320  pages,  50c. 


TEACHERS     HANDBOOK 

giving  oral  work  preparatory  for  Book  I.,  suggestions  to 
teachers  who  are  using  The  Werner  Arithmetics,  answers  to 
problems  in  Books  II.  and  III.,  and  a  large  amount  of  supple- 
mentary seat-work.    Cloth,  137  pages,  25c. 


THE    HALL    ARITHMETICS 

A  Two-Book  Course  for  Graded  or  Ungraded  Schools 

Hall's  Elementary  Arithmetic,  cloth,  248  pages,  -       -       35c. 
Hall's  Complete  Arithmetic,  cloth,  448  pages,  -       -       -   60c. 


''H  PEP'y- 


Copyright,  1901,  by 
FRANK  H.  HALL 


SfjE  ILakcsitiE  ^ress 

R.  R.  DONNELLEY  &  SONS  COMPANY 
CHICAGO 


SUGGESTIONS  TO  TEACHERS  AND  PARENTS. 


CHAPTER  I. 

Note  1. — Most  pupils  on  entering  school  are  somewhat  familiar  with 
the  number  idea.  A  majority  of  children  at  six  years  of  age  can  separate 
from  a  group,  four,  five,  or  six  objects.  Some  can  count,  with  a  good  degree 
of  accm-acy,  ten  or  twelve  objects.  It  is  therefore  unnecessary,  except  in 
rare  cases,  for  the  teacher  of  first-grade  pupils  to  spend  time  in  trying  to 
"  develop  the  idea  of  five  "  or  six.  The  work  suggested  in  this  chapter,  then, 
is,  (1)  for  mothers,  (2)  for  teachers  of  backward  pupils,  and  (3)  for  a  review 
of  that  with  which  many  of  the  pupils  in  all  first  grades  are  akeady  familiar. 

1.    Train  the  child  to  distmguish  one  object  from  two  objects. 

Bring  one  apple.  Bring  two  apples.  Bring  two  pencils.  Bring 
one  pencil.  Hold  up  one  hand.  Hold  up  two  hands.  Show  me  one 
thumb.  Show  me  two  thumbs.  Give  Mag  one  cherry.  Give  John  tivo 
cherries.     Make  one  mark.     Make  tioo  marks.     How  many  horses? 

How  many  marbles?     One  apple  and  one  apple  are  .      One 

book  and  one  book  are .      One  boy  and  one  boy  are  . 

With    two   objects  in  view,  the  attention  of   the  child   being 

directed  to  them,  say:     One  and  one  are .     Repeat  many  times, 

using  a  variety  of  objects. 

With  the  objects  concealed  from  view,  but  presumably  imaged 

by  the  child,  say:      One  and   one  are  .      Repeat   many   times, 

taking  care  that  at  first  there  come  into  the  :nuid  of  the  child  images 
of  two  certain  objects  suggested  by  the  words,  One  and  one. 

XoTE  2. — The  care  suggested  in  the  foregoing  is  necessary  lest  the 
child  shall  simply  memorize  the  expression.  One  and  one  are  two,  without 
thinking  its  meaning.  The  attention  of  the  author  was  once  called  to  a  pupil 
who  was  able  to  recite  a  hundred  number  statements  like.  Four  and  four 
are  eight,  one  half  of  four  is  two,  four  is  one  half  of  eight,  and  who  yet  had  no 
knowledge  of  number  whatever — could  not  select  two  or  three  objects  from  a 
group.  It  is  a  common  experience  to  find  pupils  in  the  second  and  third 
grades  who  have  memorized  number  facts  without  perceiving  them. 


54NI7 


IV 

Note's.'— At  this  stage  of  the  work  the  child  should  see  number  as  mag- 
nitude. The  one  is  to  him  one  book,  one  apple,  one  marble,  one  boy.  Later 
he  will  learn  to  see  number  as  ratio. 

"  The  formulae  of  arithmetic  and  algebra  are  capable  of  double  interpre- 
tation. For  instance,  such  a  symbol  as  3  meant,  in  the  first  place,  a  number 
of  letters  or  men  or  any  other  thing ;  but  afterwards  was  regarded  as  mean- 
ing an  operation,  namely,  that  of  trebling  anything." — Common  Sense-  of  the 
Exact  Sciences,  D.  Appleton  &  Company. 

2.  Make  the  child  familiar  with  the  number  three;  and  with  the 
fact  that  two  and  one  are  three.  In  doing  this  work,  observe  the 
same  order  as  that  suggested  in  the  preceding  section. 

(a)  Use  objects  and  name  them  in  connection  with  the  numbers 
employed;  as,  Bring  two  ajjples,  Bring  three  apples.  Give  May  two 
cherries.  Give  John  three  cherries,  Show  me  two  fingers,  Show  me  three 
fingers,  Two  marUes  and  one  marUe  are  three  marlles,  One  look  and 
two  hooks  are  three  books. 

(b)  Use  objects  but  do  not  name  them;  thus,  with  two  marbles 
and  one  marble  before  the  pupil,  lead  him  to  say.  Two  and  one  are 
three.  One  and  two  are  three. 

(c)  Conceal  the  objects  and  lead  the  pupil  to  image  them,  and 
say,  Two  and  one  are  thixe,  One  and  tvjo  are  three. 

Note  4. — To  assist  the  pupil  in  imaging  objects  (as  two  marbles  and  one 
marble),  these  may  be  exhibited  and  immediately  concealed  from  view  just 
before  the  child  is  required  to  say,  Tico  and  one  are  three.  He  makes  this 
statement  of  a  number  fact  and  thinks  (images)  marbles.  Later  this  will  not 
be  necessary,  for  he  will  early  learn  the  generalization  that  tico  and  one  are 
three,  no  matter  what  may  be  the  objects  to  which  these  numbers  are  applied. 
But  he  must  arrive  at  this  conclusion,  not  by  memorizing  the  words  that 
express  the  fact,  but  by  thinking  it  in  connection  with  a  variety  of  objects. 

Note  5. — To  lead  the  pupil  to  think  that  two  and  one  are  three,  it  is  not 
best,  at  first,  to  ask  how  many  two  and  on«  are.      Rather,  let  the  teacher  say. 

Two  and  one  are ,  and  allow  the  pupil  to  complete  the  statement.     This 

simplifies  the  work,  since  it  relieves  the  pupil  of  the  necessity  of  interprettng 
a  question  and  framing  an  answer.  It  allows  him  to  concentrate  his  thought 
upon  the  number  fact.  When  he  is  familiar  with  many  number  facts  he  will 
be  able  to  interpret  and  to  answer  questions  concerning  them.  One  of  the 
most  common  errors  in  arithmetical  teaching  is  the  attempt  to  have  a  child 
"  express  in  good  English  "  and  in  complete  sentences  that  which  he  does  not 
perceive. 


For  reasons  that  will  now  be  apparent,  the  attention  of  young  pupils  may- 
be directed  to  unfamiliar  number  facts  by  means  of  the  incomplete  assertion 
better  than  by  the  interrogative  sentence. 

3.  The  attention  of  the  child  may  now  be  directed  to  four 
objects.  Following  the  plan  outlined  on  the  preceding  pages,  he 
should  learn  that  three  and  one  are  four,  that  one  and  three  are 
four,  that  two  and  two  are  four,  and  that  two  twos  are  four. 

XoTE  6. At  this  stage  of  the  work,  the  author  does  not  deem  it  advisable 

to  employ  figures  or  written  words  to  represent  number.  For  some  time — 
many  weeks,  possibly  many  months — let  the  spoken  word  be  the  only  number 
symbol  employed.  This  will,  on  the  one  hand,  minimize  the  danger  of  lead- 
ing the  pupil  into  symbol  juggling— the  use  of  empty  figm-e  symbols;  and  on 
the  other  hand,  will  avoid  the  exhaustion  of  the  child's  strength  (which  for 
the  moment  we  desire  to  employ  in  the  seeing  of  magnitude  relation  and 
expressing  it  numerically)  in  the  recognition  and  pronunciation  of  written  or 
printed  words. 

4.  The  idea  of  half  may  now  be  taught. 

Give  sister  half  of  your  candy.  Give  me  half  of  your  apple. 
Give  Henry  half  of  your  clay.  Continue  such  work  until  the  child 
is  familiar  with  the  fact  that  the  halves  of  anything  are  alike  as  to 
quantity. 

Give  the  child  four  toothpicks.  Then  say,  Give  me  half  of  the 
toothpicks.    Do  the  same  with  two  toothpicks;  with  three  toothpicks. 

]>foTE  7. — If  this  work  is  properly  performed,  little  will  need  to  be  told 
the  child  or  done  for  the  child.  As  soon  as  he  understands  what  you  mean 
by  half,  he  can  find  half  of  four  toothpicks,  half  of  two,  and  half  of  three. 
Later,  he  will,  without  assistance,  find  half  of  six,  half  of  five,  half  of  eight, 
half  of  seven,  half  of  a  foot,  half  of  six  inches,  half  of  five  inches,  half  of  a 
half,  etc.  It  is  the  idea  of  half  that  is  to  be  taught;  then  the  child  should  be 
allowed  to  do — to  find  half  of  many  things  and  of  many  groups  of  things. 
He  will  easily  memorize  some  of  the  number  facts  which  he  perceives ;  not  by 
remembering  the  words  that  express  them,  but  by  imaging  the  related  magni- 
tudes.    When  you  say.  Half  of  four  is  ,  he  should  see  with  the  mind's 

eye  the  four  (objects)  in  two  equal  groups.  He  then  tells  you  what  he  sees ; 
namely,  that  half  of  four  is  two.  It  is  an  image  that  he  remembers,  not  a 
plii'ase  or  sentence. 

5.  The  child  may  learn  to  count  to  ten ;  or,  if  this  is  done  with 
little  effort,  to  twenty,  or  even  to  a  hundred. 


"WTien  he  is  able  to  take  ten  objects  from  a  group,  he  may  be 
allowed  to  put  toothpicks  in  bunches  of  ten.  These  may  be  held 
together  by  little  rubber  bands.  He  may  learn  that  two  tens  are 
tiventy;  three  tens,  thirty;  four  tens,  forty,  etc.  He  may  do  this 
even  before  he  can  count  from  ten  to  twenty.  He  \nl\  then  be  able 
to  tell  you  that  half  of  forty  is  twenty,  and  that  half  of  twenty  is  ten. 

Note  8. — A  necessary  caution  in  connection  with  the  foregoing  is,  that 
the  child  should  not  be  allowed  to  think  that  saying  the  names  of  the  num- 
bers in  regular  order  is  counting.  Neither  must  he  be  permitted  to  entertain 
the  idea,  for  instance,  that  the  ninth  object  is  /n'ne;  the  tenth  object  ten,  etc. 
He  can  "count  to  ten"  if  he  can  take  from  a  group  of  more  than  ten  objects 
any  number  of  objects  not  greater  than  ten  that  may  be  suggested.  He  may 
be  able  to  bring  twenty  objects  (two  tens)  or  thirty  (three  tens)  or  forty 
(four  tens)  before  he  can  "  count  to  twenty." 

6.  Work  with  the  number  fve.  Lead  the  child  to  discover  that 
two  fires  are  ten;  that  one  half  of  five  is  ttco  and  one  half;  tlmt  four 
and  one  are  five;  that  three  and  tv:o  are  five;  that  tivo  twos  and  one 
are  five. 

As  soon  as  the  child  perceives  one  of  the  above  number  facts,  he 
should  be  encouraged  to  remember  it.  This  he  should  do  by  recalling 
his  image  of  the  objects  so  grouped  as  to  suggest  the  fact  to  be 

remembered.     Thus,  the  -words,   One  half  of  five  is  ,  should 

bring  into  his  consciousness  an  image  of  five  objects  in  two  equal 
groups. 

XoTE  9. — In  Note  4  the  use  of  a  variety  of  objects  for  the  pm-pose  of 
leading  the  pupil  to  abstract  the  idea  of  number  and  to  generalize  num- 
ber facts,  is  recommended.  But  in  teaching  a  particular  number  fact,  imi- 
formity  of  objects  is  preferable  to  variety.  Moreover,  the  objects  employed 
should"^  be  simple  and  unattractive  in  themselves.  For  this  early  work, 
nothing  can  be  better  than  ordinary  toothpicks.  They  are  inexpensive,  may 
be  broken  into  halves  or  thirds  or  fourths,  are  easily  grouped,  and  may  be 
conveniently  put  up  in  packages  of  ten. 

"  The  mental  comprehension  of  number  is  disturbed  if  things  which 
awaken  other  ideas  or  desires  are  employed.  The  mind  is  capable  of  only  a 
certain  amount  of  interest,  and  when  this  interest  is  wholly  or  partly  with- 
drawn, but  little  can  be  expected  for  the  particular  thing  at  hand.  For  this 
reason,  while  teaching  the  abstract  number  there  should  be  but  few  things 
shown  the  child,  and  these  should  be  simple  and  uniformly  the  same." — Levi 
Seeley,  in  Gruhe's  Method  of  Teaching  Arithmetic. 


7,  Work  with  the  number  six.  The  child  should  now  discover 
and  memorize  the  following  number  facts:  Five  and  one  are  six. 
Four  and  two  are  six.  Three  and  three  are  six.  Ttvo  threes  are  six. 
One  half  of  six  is  three.     Tliree  ttvos  are  six. 

He  may  be  taught  to  think  of  tivo  as  one  third  of  six;  and  of 
fo2ir  as  two  thirds  of  six. 

He  may  learn  to  count  to  twelve  if  he  has  not  already  done  so; 
and  then  he  may  discover  and  memorize  the  fact  that  two  sixes  are 
twelve. 

8.  Teach  the  figures  from  1  to  12.  Give  the  child  a  foot  rule, 
and  help  him  to  become  familiar  with  the  terms,  inch  and/oo^. 

Teach  him  to  use  the  rule  in  measuring.  At  first  let  him 
measure  distances  that  are  an  integral  number  of  feet  or  an  integral 
number  of  inches. 

Later,  teach  him  the  meaning  and  use  of  the  expressions,  tivo 
and  one  half  feet,  two  and  one  half  inches,  three  and  one  half  inches, 
four  and  one  fourth  inches,  four  and  three  fourths  inches,  etc.  Follow 
this  by  encouraging  him  to  measure  distances  suggested  by  the  above 
expressions. 

Help  him  to  discover  that  one  half  is  tioo  fourths;  that  one  half 
and  one  fourth  are  three  fourths;  that  there  are  four  fourths  in  a 
ivhole. 

With  the  rule  concealed  from  view,  ask  him  to  draw  a  line  two 
inches  long;  a  line  three  inches  long,  etc.  Then  allow  him  to  test 
his  work  by  applymg  the  rule  to  the  lines  he  has  drawn. 

He  may  be  told  that  a  dozen  is  tvjelve.  He  may  then  discover 
that  half  a  dozen  is  six;  that  a  fourth  of  a  dozen  is  three;  that  three 
fourths  of  a  dozen  are  nine. 

Note  10. — While  doing  the  above  number  work,  the  pupil  must  not  be 
allowed  to  lose  sight  of  magnitude.  There  must  be  no  attempt  to  have  him 
memorize  the  words,  one  half  and  one  fourth  are  three  fourths.  He  must 
rather  discover  this  number  fact  and  remember  it,  at  first,_  by  recalling  his 
image  of  the  rule  and  its  divisions ;  or  of  a  pie  and  its  divisions. 

Note  11. — The  foregoing  pages  suggest  what  the  average  child  may 
easily  learn  concerning  number  by  the  time  he  is  six  years  of  age.  It  is  not 
expected  that  the  mother  will  present  this  to  the  child  in  formal  number 
lessons  in  the  exact  order  here  given,  but  rather  that,  beginning  when  the 


child  is  three  or  four  years  of  age,  she  will  incidentally,  in  connection  with 
his  play  or  her  own  work,  lead  the  child  to  perceive  the  number  facts  herein 
given  and  to  retain  them  in  mind  hy  means,  chiefly,  of  his  memory  images  of 
the  magnitudes  considered. 

Besides  the  mere  counting,  there  are  less  than  fifty  of  these  number  facts 
suggested.  One  fact  learned  each  week,  the  work  will  be  accomplished  in  a 
year.  Some  children  may  learn  much  more  than  the  amount  here  suggested ; 
but  if  all,  before  entering  school,  could  be  introduced  to  the  subject  somewhat 
after  the  manner  herein  suggested,  the  number  of  pupils  thought  to  be  "  born 
short "  in  respect  to  mathematical  power  would  be  greatly  diminished. 

Note  12. — If  the  first-grade  teacher  finds  pupils  in  her  class  who  are 
seemingly  "deficient  in  the  number  sense,"  she  should  make  a  careful  study 
of  each  case ;  and,  using  the  foregoing  pages  as  suggestive  of  the  order  of 
procedure,  should,  in  connection  with  the  natm-e  work,  the  drawing,  the  dis- 
tribution of  material,  the  paper-folding,  etc.,  help  the  child  to  see  magnitude 
relation  in  a  small  way,  and  to  express  it  numerically. 


CHAPTER  II. 
THE   FIRST  YEAR   OF   SCHOOL. 

Note  1. — Soon  after  the  beginning  of  school  the  teacher  should  carefully 
note  the  real  number  knowledge  which  each  pupil  possesses.  It  is  not  the 
knowledge  and  power  of  the  class  as  a  whole  that  the  teacher  must  discover, 
but  rather  the  number  knowledge  of  the  individual.  In  making  these  discov- 
eries the  teacher  should  make  use  of  the  suggestions  in  Chapter  I.  Pupils 
who  have  mastered  the  work  there  outlined  may  safely  engage  in  work  sug- 
gested by  the  following  topics. 

XoTE  2. — The  number-work  of  the  first  school  year  should  be  mainly 
oral,  should  occupy  comparatively  little  of  the  pupil's  time,  and  should  be 
presented  incidentally  in  connection  with  (1)  the  administrative  duties  of  the 
teacher,  (2)  the  nature  work,  (3)  constructive  work,  and  (4)  reading. 

XoTE  3. — No  attempt  is  made  to  give  these  topics  in  the  order  in  which 
the  work  should  be  presented.  Any  one  of  the  subjects  may  be  introduced 
when  the  pupil  seems  ready  for  the  little  problems  given  and  especially 
when  he  feels  the  need  of  number  knowledge  in  order  that  he  may  perform 
some  task  assigned.  The  thoughtful  teacher,  however,  will  always  keep  in 
mind  the  work  done  by  each  pupil,  and  will  see  that  it  is  frequently  reviewed, 
and  that  each  new  step  is  in  some  way  related  to  that  with  which  the  child 
is  already  familiar. 

I.— ADMINISTRATION. 

1.  Attendance.  How  many  girls  tardy  ?  How  many  boys  tardy  ? 
How  many  pupils  tardy  ?  How  many  girls  absent  ?  How  many  boys 
absent  ?  How  many  pupils  absent  ?  How  many  boys  present  in 
Eow  1  ?  How  many  girls  present  in  Row  1  ?  How  many  pupils 
present  in  Row  1  ?  ^  How  many  more  pupils  present  in  Row  1  than 
in  Row  2  ?  ^Miich  is  the  larger,  Class  A  or  Class  B  ?  How  many 
pupils  in  Class  A?  How  many  pupils  in  Class  B?  How  many 
pupils  absent  from  Class  B  ?     How  many  pupils  present  in  Class  C  ? 

2.  Distribution  of  Materials.  A  monitor  from  each  row  goes  to 
the  teacher  for  pencils,  sheets  of  paper,  scissors,  crayons,  or  books. 
How  many  do  you  need  ?     Teacher  gives  some  to  one  of  the  moni- 


tors.  How  many  have  you  ?  Do  you  need  as  many  as  you  have  ? 
Do  you  have  as  many  as  you  need  ?  Eeturn  to  me  all  you  do  not 
need.  Monitor  goes  to  the  supply  and  counts  for  himself  under  the 
eye  of  the  teacher.  Count  by  ones.  Count  by  twos.  Count  by 
threes.  Carry  books  to  Room  2.  How  many  can  Mary  carry  ? 
How  many  can  John  carry  ?  How  many  did  Mary  carry  ?  How 
many  did  John  carry  ?  How  many  more  did  John  carry  than  Mary  ? 
3.  Time.  Observe  the  clock  face  for  one  minute ;  for  five 
minutes.  Tell  the  pupils  how  far  the  long  hand  moves  in  one  hour. 
Observ^e  how  far  the  short  hand  moves  in  an  hour.  Teach  the 
figures  on  the  dial.  How  far  does  the  long  hand  move  in  half  an 
hour  ?  In  a  quarter  of  an  hour  ?  A  quarter  of  an  hour  is  fifteen 
minutes.  A  half  hour  is  thirty  minutes.  An  hour  is  sixty  minutes. 
Count  by  fives  to  fifteen ;  to  thirty ;  to  sixty.  Ten  is  how  many 
fives  ?  Fifteen  is  how  many  fives  ?  In  five  minutes  you  may  have 
a  recess ;  watch  the  clock.  Observe  the  position  of  the  hands  when 
school  begins  ;  at  the  beginning  of  the  recess ;  at  the  end  of  the 
recess ;  at  the  close  of  school ;  do  this  for  both  forenoon  and  after- 
noon.    Five  minutes  and  one  minute  are .     Ten  minutes  and 

one  minute  are .     Fifteen  minutes   and  one   minute   are . 

Five  minutes  and  two  minutes  are .    Five  and  three?     Five  and 

four  ?  Ten  and  two  ?  Ten  and  three  ?  Ten  and  four  ?  Ten  and 
five  ?  Fifteen  and  two  ?  Fifteen  and  three  ?  Fifteen  and  four  ? 
Fifteen  and  five  ?  John  is  how  many  minutes  tardy  ?  What  time 
do  you  start  for  school  ?  In  how  many  minutes  can  you  come  to 
school  ?  How  many  hours  of  school  each  day  ?  At  what  time  are 
you  dismissed  ?  How  many  days  of  school  each  week  ?  How  many 
days  of  each  week  do  you  remam  at  home  ?  A  week  is  how  many 
? 


Note  4. — Do  not  attempt  to  give  all  of  the  foregoing  regularly  and  on 
consecutive  days,  before  attempting  much  that  follows  this  topic.  Rather, 
introduce  portions  of  the  suggested  matter  incidentally  in  connection  with 
and  as  a  part  of  the  administrative  work. 

But  whenever  a  number  fact  that  should  be  memorized  has  been  given,  the 
teacher  should  hold  it  in  her  own  mind  for  fi-equent  review.  So  far  as 
possible  she  should  know  the  memory  possessions  of  each  pupil ;  and,  taking 
care  that  he  loses  nothing  of  what  he  has  already  acquired,  she  shoiUd  see  to 


it  that  a  little,  from  time  to  time,  is  added  thereto.  The  careless  teacher 
allows  a  pui>il  to  forget  almost  as  much  as  he  memorizes  dm-iug  a  term. 
This  is  usually  the  case  with  some  pupils  when  the  teacher  presents  the 
memory  work  to  the  class  as  a  whole  and  loses  sight  of  the  individual  pupil. 
The  teacher  should  constantly  ask  herself :  How  much  more  does  Mary^  know 
to-day  than  slie  knew  yesterday?  "What  does  William  need  to  review  in 
order  that  he  may  be  ready  for  the  new  number  fact?  "What  has  John  per- 
ceived and  memorized? 

II.— NATURE   STUDY. 

1.  Plants.  Count  buds,  leaves,  petals,  etc.  Measure  growth  of 
twigs.  Measure  length  of  needles  from  pine  trees;  from  spruce 
trees;  from  fir  trees.  Find  circumference  of  trees  in  school  yard. 
Find  growth  of  corn  or  of  a  vine  for  one  day ;  for  one  week. 

2.  Animals.  Count  legs  of  fly,  spider,  cray-fish,  beetle.  How 
many  legs  have  two  toads  ?  Two  butterflies  ?  Two  spiders  ?  Three 
cray-fish  ?  Three  frogs  ?  Three  beetles  ?  How  many  toes  on  a  cat's 
fore-foot?  On  hmd-foot  ?  On  two  fore-feet?  On  two  hind-feet? 
How  many  shoes  does  a  horse  need  ?  A  pair  of  horses  ?  How  many 
shoes  does  an  ox  need  ?  A  yoke  of  oxen  ?  How  tall  is  your  pony  ? 
(To  be  measured  over  the  front  feet  to  top  of  shoulder.)  How  tall 
are  you  ? 

3.  Weather  Record.  Number  of  clear,  cloudy,  and  rainy  days  in 
the  week ;  in  the  month.  Prevailing  winds.  How  many  days  was 
there  a  west  wind?  An  east  wind?  A  north  wind  ?  A  south  wind? 
A  northeast  wind  ?  A  northwest  wind  ?  A  southeast  wind  ?  A 
southwest  wind  ?  How  many  days  did  it  rain  last  month  ?  How 
many  this  month  ?  How  many  more  last  month  than  this 
month?  To-day  is  Monday;  last  Friday  was  May  sixth;  what 
month  and  day  of  the  month  to-day  ?  Teach  pupils  to  read  the 
thermometer.  Eepresent  the  thermometer  scale  on  blackboard,  one 
inch  equal  two  degrees.  Mark  daily  readings.  Piepresent  five 
thermometer  scales  side  by  side  on  blackboard.  Mark  the  reading 
Monday  at  twelve  o'clock  on  first  scale ;  Tuesday  at  same  hour  on 
second  scale,  etc.  At  end  of  week  connect  the  points  of  daily  mark- 
ing, thus  gi^"ing  a  graphic  representation  of  variation. 

IN'oTE  5. — The  pupils  will  be  interested  in  noting  the  variation  of  the 
outdoor  temperatm-e  during  a  school  day.     Put  eight  scales  side  by  side  on 


Xll 


blackboard.  On  the  first,  mark  the  standing  at  nine  o'clock ;  on  the  second, 
at  ten  o'clock,  etc.  Connect  the  points  of  hourly  marking.  Then  ask :  At 
■what  time  was  it  -warmest?  How  many  degrees  warmer  was  it  at  twelve 
o'clock  than  at  nine  o'clock?     At  three  o'clock  than  at  nine  o'clock? 


Ill — CONSTRUCTIVE  AVORK. 

1.  Drawing.  Draw  a  horizontal  line  one  inch  long;  two  inches 
long ;  three  inches  long.  Draw  a  vertical  line  one  inch  long ;  three 
inches  long.  Draw  two  parallel  horizontal  lines  three  inches  long 
and  one  inch  apart.  Draw  several  parallel  vertical  lines  one  half 
inch  apart  and  two  inches  long.     Draw  a  four-inch  line;  bisect  it. 

One  half  of  four  inches  is  .     Draw  a  five-inch  line;  bisect  it. 

One  half  of  five  inches  is  .     Draw  a  one-inch  square.     Draw 

a  two-inch  square  and  divide  it  into  one-inch  squares.     A  two-inch 

square  is  equal  to one-inch  squares.    Draw  a  three-inch  square; 

di\dde  it  into  one-inch  squares.    A  three-inch  square  is  equal  to 

one-inch  squares.  Draw  an  oblong  one  inch  by  three  inches ;  divide 
it  into  one-iach  squares.  Draw  an  oblong  two  inches  by  three 
inches;  divide  it  into  one-inch  squares.  Divide  a  one-inch  square 
into  half-inch  squares.  How  many  half-inch  squares  in  a  one-inch 
square  ? 

Note  6. — In  doing  the  work  suggested  in  the  foregoing  paragraph  at 
first  allow  the  pupil  to  use  a  ruler;  then  require  him  to  draw  without  a  guide 
and  to  test  his  work  with  the  ruler  or  with  paper  of  known  dimensions. 

Note  7. — After  the  pupil  has  drawn  a  figure  several  times  he  should 
be  able  easily  to  bring  the  image  of  the  figm-e  into  consciousness  when  its 
description  is  given  by  the  teacher.  Thus,  when  the  teacher  says,  "Imagine 
a  two-inch  square ;  divide  it  into  one-inch  squares,"  the  pupil  should  see  all 
the  lines  with  the  mind's  eye  almost  as  clearly  as  they  would  be  seen  were 
the  figure  on  the  blackboard  in  plain  view.  If  he  images  well  he  will  be  able 
to  tell,  without  drawing,  the  number  of  one-inch  squares  in  a  two-inch  square ; 
the  number  of  two-inch  horizontal  lines,  and  the  number  of  two-inch  vertical 
lines,  in  the  figure.  Cultivate  from  the  first  the  imaging  power.  To  answer 
the  question,  "  A  three-inch  square  equals  how  many  one-inch  squares  ?  "  by 
word  memory  is  valueless ;  to  answer  by  drawing  the  figure  and  counting  the 
squares  is  better ;  to  answer  by  imaging  the  figure  and  counting  the  squares 
is  best.     First-grade  pupils  can  be  taught  to  image  such  figm-e& 


2.    Paper  Folding. 

paper.     How  wide 


Give    to    each    pupil  a  four-inch    square    of 
How  long  is  the  paper?     How 


is  the  paper? 
many  corners  ?     How  many  edges  ? 

Fold  the  right  edge  upon  the  left  edge.  Crease.  Unfold.  How 
many  oblongs?  How  wide  is  each  oblong?  How  long  is  each 
oblong?     Each  oblong  is  what  part  of  the  four-inch  square? 

Fold  the  right  edge  of  the  paper  to  the  crease;  the  left  edge. 
Unfold.  How  many  oblongs?  How  wide  is  each  oblong?  How 
long  is  each  oblong?  Each  oblong  is  what  part  of  the  four-inch 
square  ?  ) 

Fold  the  lower  edge  upon  the  upper  edge.  Unfold.  How  many 
oblongs?  How  wide  is  each  oblong?  How  long  is  each  oblong? 
Each  oblong  is  what  part  of  the  four-inch  square  ?  One  half  is  how 
many  eighths?  A  fourth  is  how  many  eighths?  Two  fours  are 
.     Four  twos  are . 

Fold  the  lower  edge  of  the  paper  to  the  crease;  the  upper  edge. 
Unfold.  What  is  the  size  of  each  httle  square  ?  How  many  one- 
inch  squares  in  one  row?  How  many  rows?  How  many  one-inch 
in   all?     How    many    one-inch    squares    equal  a  four-mch 


squares 

square?     Four  fours  are  , 

fourth  of  sixteen  is 
four  and  four  are  — 


One  half  of  sixteen  is  .     One 

Two  eifrhts  are .     Four  and  four  and 


Fif 

.  3. 

' J 

Note  8. — By  cutting  the  paper  as  indicated  by  the  heavy  lines  in  Fig.  1, 
and  folding  and  pasting  the  corner  squares,  an  open  box  two  inches  by  two 
inches  by  one  inch  may  be  made. 

Note  9. — By  cutting  tlie  paper  as  indicated  by  the  heavy  lines  in  Fig.  2, 
and  folding  and  pasting,  a  square  prism  one  inch  by  one  inch  by  two  inches 
may  be  made. 


Note  10. — By  cutting  the  paper  as  indicated  by  the  heavy  lines  in  Fig. 
3,  discarding  the  four  ujDper  squares,  and  folding  and  pasting  the  lower  tliree 
fourths  of  the  sheet,  a  one-inch  cube  may  be  made. 

Note  11 — By  using  an  eight-inch  square  of  paper,  folding  and  cutting 
as  indicated  by  Fig,  1,  an  open  box  four  inches  by  four  inches  by  two  inches 
may  be  made. 

Note  12.— By  using  an  eight-inch  square  of  paper,  folding  and  cutting  as 
indicated  by  Fig.  2,  a  square  prism  two  inches  by  two  inches  by  four  inches 
may  be  made. 

Note  13. — By  using  an  eight-inch  square  of  paper,  folding  and  cutting 
as  indicated  by  Fig.  3,  a  two-inch  cube  may  be  made. 

Note  14. — By  using  a  twelve-inch  square  of  paper,  folding  and  cutting  as 
indicated  by  Fig.  3,  a  three-inch  cube  may  be  made. 

3.   Building  with  One-inch  Cubes. 

Note  15. — Provide  at  least  twenty-seven  one-inch  cubes,  a  two-inch  cube, 
a  three-inch  cube,  a  square  prism  one  inch  by  one  inch  by  two  inches,  a  square 
prism  one  inch  by  one  inch  by  three  inches,  a  square  prism  two  inches  by  two 
inches  by  three  inches,  and  a  rectangular  prism  one  inch  by  two  inches  by 
three  inches.     These  should  be  made  of  wood. 

A  cube  has faces.    Each  face  of  a  cube  is  a  square.    A  cube 

has corners.    A  cube  has edges.    Three  edges  meet  at  each 

corner. 

A  square  prism  has faces.     Two  of  the  faces  are  squares. 

Four  of  the  faces  may  be  oblongs.     Some  prisms  have  no  square  faces. 

A  face  of  a  two-inch  cube  is  a  two-inch  square.  A  two-inch 
square  equals one-inch  squares. 

A  face  of  a  three-inch  cube  is  a  three-inch  square.  A  three-inch 
square  equals one-inch  squares. 

A  two-inch  cube  equals one-inch  cubes.     A  three-inch  cube 

equals one-inch  cubes. 

One  half  of  a  two-inch  cube  equals  one-inch  cvibes.     One 

fourth  of  a  two-inch  cube  equals  one-inch  cubes.     One  eighth 

of  a  two-inch  cube  equals  a cube. 

Note  16. — In  the  beginning  the  child  must  work  with  sense  magnitudes; 
but  very  early  he  can  be  taught  to  build  with,  separate  into  parts,  and  compare 
imaged  magnitudes.  To  this  end  the  teacher  and  pupil  must  frequently  talk 
about  seuse  magnitudes  that  are  present  to  the  mind's  'eye  only.     The  pupil 


must  be  led  to  see  the  four  sides  of  a  one-inch  square,  or  of  a  two-inch  square ; 
the  six  square  faces  of  a  one-inch  cube,  or  of  a  two-inch  cube ;  the  four  one- 
inch  squares  in  the  face  of  a  two-inch  cube ;  tlie  eight  one-inch  cubes  in  a 
two-incli  cube ;  and  the  twenty-seven  one-inch  cubes  in  a  three-inch  cube, 
tvliile  all  these  objects  are  concealed  from  view.  At  this  stage  of  the  work  the 
niatlieniatical  skill  of  the  pupil  depends  mainly  upon  his  ability  to  call  the 
images  of  magnitudes  into  consciousness  when  the  symbols  of  these  (their 
names  or  descriptions)  are  spoken  by  the  teacher. 

lY.— READING. 

1.  Pages.  Teach  the  child  to  find  the  page  by  number.  How 
many  pages  did  you  read  yesterday?  Upon  what  page  do  you  begin 
to-day  ?  If  you  read  two  pages  to-day,  upon  what  page  will  you 
begin  to-morrow?  Henry  is  reading  on  page  28.  Mary  is  reading 
on  page  32.  Mary  is  how  many  pages  in  advance  of  Henry?  How 
many  pages  must  you  read  before  you  reach  page  40  ?     How  many 

pages  in  your  book  ?     Twenty  pages  and  twenty  pages  are . 

30  and  20?  50  and  50?  50  and  20?  29  and  1?  29  and  2  ? 
39  and  1  ?     39  and  2  ? 

2.  Lines.  Find  the  first  line  on  the  page;  the  second  line;  the 
third  line,  etc.  Eead  the  fourth  line.  Kead  the  second  line.  Find 
the  third  line  on  page  21.  Find  the  fourth  line  from  the  bottom  of 
'the  page.     How  many  lines  on  page  15  ? 

3.  Words.  How  many  words  in  the  word  list  at  the  beginning 
of  lesson  ?  How  many  words  in  the  first  line  ?  In  the  second  line  ? 
Find  the  third  word  in  the  second  line.  Can  you  find  the  word  tu-o? 
How  many  times  does  the  word  two  occur  on  page  10? 

4.  Letters.  How  many  letters  in  the  word  John  ?  In  the  word 
aijple  ?  Fmd  the  longest  word  on  page  10.  How  many  letters  in 
the  longest  word  on  page  12  ?  How  many  words  can  you  think  of, 
each  of  which  is  made  of  two  letters  ?  Of  three  letters  ?  Of  four 
letters  ? 

Note  17. — The  Pedagogical  Pause.  We  have  grammatical  pauses  and 
rhetorical  pauses.  There  is  yet  another  pause  that  may  very  properly  be 
called  the  pause  pedagogical.  It  is  the  pause  that  the  teacher  should  make  as 
a  pedagogical  necessity  in  questions  and  statements  to  pupils.  This  pause 
should  follow  a  word  or  phrase  which  sj-mbolizes  something  that  maybe  diffi- 
cidt  for  the  hearer  to  image.     The  length  of  the  pause  should  be  measured 


by  the  time  required  by  the  pupil  to  image  that  for  which  the  word  or  phrase 
stands.  This  pause  is  indicated  in  the  following  sentences  by  the  double 
asterisk : 

The  written  word  hoy  *  *  contains  how  many  letters  ? 

One  half  of  a  foot  *  *  is  how  many  inches? 

How  many  half  inches  *  *  in  three  inches  ? 

One  half  oifour  toothpicks  *  *  is 

One  half  of  three  toothpicks  *  *  is 

Think  of  a  two-inch  square  *  *  Divide  it  into  one-inch  squares  *  *  How 
many  one-inch  squares? 

How  many  one-inch  squares  of  paper  *  *  do  you  need  to  make  a  three-inch 
square  ? 

How  many  one-inch  cubes  *  *  do  you  need  to  build  a  two-inch  cube? 

A  four-inch  cube  **  equals  how  many  two-inch  cubes? 

A  four-inch  square  **  equals  how  many  two-inch  squares? 

A  ttoo-inch  cube  *  *  equals  how  many  one-inch  cubes? 

A  two-inch  square  **  equals  how  many  one-inch  squares? 

With  the  bright  pupil  this  pause  may  be  made  very  short.  With  the  dull 
pupil  it  should  be  made  very,  very  long.  With  any  pupil  it  must  be  made 
long  enough  for  him  to  image  that  for  which  the  icord  symbols  stand.  To 
proceed  without  the  imaging  on  the  part  of  the  pupil,  is  to  tempt  him  into 
word  memory  work.  A  proper  observance  of  this  pause  and  special  attention 
to  the  imaging  power  of  individual  pupils  can  not  fail  to  promote  better 
teaching  in  elementary  number-work. 

Note  18. — It  will  be  observed  that  the  child  has  already  reached  a  point 
at  which  a  kind  of  double  imaging  is  necessary.  The  teacher  may  speak  the 
word  "  cube  "  when  she  desires  to  bring  into  the  consciousness  of  the  child  an 
image  of  the  written  word  cube.  Again,  she  may  speak  the  word  "cube "  and 
desire  to  bring  into  the  consciousness  of  the  child  an  image  of  that  for  which 
the  written  word  stands.  The  teacher  must  now  strive  to  see  into  the  child 
mind  and  to  note  the  character  of  the  imaging  that  is  lieing  done.  If  the 
child  images  the  icord  cube  when  the  teacher  expects  him  to  image  that  for 
which  the  word  stands— the  real  cube — and  if  the  teacher  proceeds  on  the 
supposition  that  the  child  is  imaging  the  one  when  he  is  really  imaging  the 
other,  the  results  must  be  unsatisfactory  and  often  positively  harmful  to  the 
pupil.  The  most  practical  and  profitable  child-study  is  that  which  enables 
the  teacher  to  read  the  child  mind,  and  to  note  correctly  the  kind  and  amount 
of  imaging  activity.  The  difficult  thing  in  the  early  work  in  mathematics  is 
not,  to  see  relation,  but  to  bring  into  consciousness  images  of  the  things  related. 


CHAPTER  III. 
THE   SECOND  YEAR  OF   SCHOOL. 

The  number-work  of  the  second  school  year  must  be  done  mainly 
orally.  A  book  must  not  be  put  mto  the  hands  of  the  second  grade 
pupil  for  the  jiurpose,  of  teacJmig  Imn  numhei'  facts.  If  a  number 
book  is  used  at  all  in  this  grade,  it  should  be  made  up  of  reading 
lessons  in  which  the  child  simply  reviews  number  facts  with  which 
he  is  already  famiUar.  A  well-arranged  book  used  as  here  suggested 
will  not  only  review  number  facts,  but  will  furnish  reading  matter  in 
which  the  pupil  wiU  be  greatly  interested. 

The  Primer  of  Arithmetic  is  especially  designed  to  show  the 
order  in  which  the  number  facts  may  be  presented  orally,  and  to 
furnish  reading  lessons  in  which  the  pupil  will  be  led  to  review 
these  facts. 

The  teacher  should  take  great  care  to  prepare  the  pupil,  by  oral 
instruction,  for  the  page  he  is  to  read.  The  oral  work  should  always 
be  considerably  in  advance  of  the  reading  lesson.  In  fact,  the  second- 
grade  pupil  should  not  be  asked  to  read  statements  expressing 
number  knowledge  until  he  thoroughly  understands  the  numerical 
relations  involved.  When  he  reads,  his  task  should  be  to  recognize 
through  tlie  eye  and  to  express  that  with  which  his  ear  is  quite 
famihar.  A  good  book  used  in  the  second  grade  for  this  purpose 
will  be  helpful;  used  (in  the  hands  of  the  pupils)  to  teach  number 
facts,  it  will  be  -positively  harmful. 

If  the  lessons  herein  suggested  for  the  home  and  for  the  first 
school  year  are  properly  taught,  but  little  time  will  be  required  to 
master  the  lessons  suggested  for  the  second  school  year.  No  formal 
number-work  at  all,  in  the  first  two  years  of  school,  is  better  than 
too  much  work,  or  work  improperly  done.  Too  much  number  work 
will  give  to  the  pupil  a  bias,  on  account  of  which  magnitude  relation 
will,  ever  after,  occupy  too  prominent  a  place  in  his  thought.     Num- 


ber-work  improperly  done  will  create  a  distaste  for  such  effort,  and 
result  in  arrested  development  and  possible  permanent  injury  to  the 
pupil. 

"  It  is  perhaps  not  too  much  to  say  that  nine  tenths  of  those  who  dislike 
arithmetic,  or  wlio  at  least  feel  that  they  have  no  aptitude  for  mathematics, 
owe  this  misfortune  to  wrong  teaching  at  first." — McLellan  and  Dewey,  in 
Psychulo(iy  of  Number,  page  146. 

"  There  is  no  subject  taught  in  the  elementary  schools  that  taxes  the 
teacher's  resources  as  to  methods  and  devices  to  a  greater  extent  than  arith- 
metic. There  is  no  subject  taught  that  is  more  dangerous  to  the  pupil  in  the 
way  of  deadening  his  mind  and  arresting  its  develoi^ment,  if  bad  methods  are 
iised." — Dr.  Wm.  T.  Harris,  in  Editor's  Preface  to  Psychology  of  Number,  D. 
Appleton  &  Co. 

THE  PLAN  OF  THE  BOOK. 

The  Primer  of  Arithmetic  is  not  made  up  mainly  of  graded 
miscellaneous  problems.  It  is  built  on  a  plan.  Each  four-page 
group  constitutes  the  larger  unit  of  the  plan.  Twenty-seven  presen- 
tations of  this  gradually  changing  unit  make  up  the  book. 

In  the  first  eleven  groups  (44  pages)  the  page  units  are  as  follows: 

1st  page — New  number  facts. 

2d  page — Number  facts  applied  to  linear  measurements. 

3d  page — Number  facts  applied  to  surface  measurements. 

4th  page — The  "  Elementary  Spiral "  (a  problem  in  each  of  the 
five  fundamental  processes),  followed  by  miscellaneous  problems. 

In  the  remainder  of  the  book,  the  1st  and  4th  pages  of  each 
group  are  similar  to  the  corresponding  pages  of  the  first  eleven 
groups.  The  2d  page  teaches  the  application  of  primary  facts  to 
larger  numbers.  The  3d  page  deals  with  sohd,  surface,  linear,  and 
capacity  measurements. 

The  teacher  and  pupil  soon  discover  that  the  mastery  of  the  first 
page  of  a  group  (and  all  preceding  it)  makes  the  work  of  the  other 
three  pages  easy  and  interesting.  The  child  quickly  learns  that  it  is 
necessary  that  certain  number  facts  should  be  memorized.  The 
teacher  knows  exactly  where  to  find  these  facts,  and  is  given  definite 
direction  in  regard  to  the  order  in  which  they  should  be  presented. 

The  last  three  pages  of  each  group,  particularly  in  the  first  44 
pages,  furnish  at  ouce  a  review  of  the  newly  learned  number  facts. 


and  a  reward  for  doing  the  work  presented  on  the  1st  page  of  each 
group. 

It  will  be  observed  that  the  plan  of  the  book  is  such  that  each 
page,  between  pages  4  and  100,  sustains  a  kind  of  double  (or  quadru- 
ple) relation  to  other  parts  of  the  book.  It  is,  of  course,  related  to 
the  page  preceding  it  and  to  the  page  following  it.  It  is  also  closely 
related  to  the  4th  page  before  it  and  to  the  4th  page  after  it.  Com- 
pare page  23  with  pages  19  and  27;  page  30  with  pages  26  and  34; 
page  62  with  pages  58  and  66;  page  52  with  pages  48  and  56. 
Such  an  arrangement  as  this  greatly  aids  in  gi^^ng  to  the  child  a 
lively  sense  of  the  relation  of  the  new  to  the  old.  Moreover,  it  does 
not  allow  him  to  forget  the  fundamental  number  facts  that  are  so 
essential  to  his  progress. 

The  one  direction  to  the  teacher,  more  important  than  all  others, 
and  hence  here  repeated,  is : 

By  means  of  oral  instruction,  teach  thoroughly  every  fact  given 
in  a  4-page  group,  before  asking  or  allowing  the  pupil  to  attempt  to 
read  any  page  of  the  group. 

The  reading  thus  becomes  a  pleasant  review  (a  seeing  again),  by 
means. of  ^j/'in^ftrZ  language,  of  that  with  wdiich  the  child  is  already 
familiar  when  presented  to  him  in  spoken  language. 

It  is  the  hope  of  the  author  that  this  little  book  will  help  to 
diminish,  rather  than  increase,  the  amount  of  time  devoted  to 
number-work  in  the  first  two  grades  of  the  school.  If  the  work  is 
properly  done,  but  little  time  will  be  required  in  its  performance. 

Mere  "  figure  processes  "  are  designedly  omitted  from  most  of  the 
pages  of  the  book.  The  child  should  be  well  grounded  in  elementary 
number  processes  before  he  begins  to  practice  figure  manipulation. 
Such  nuriiber  %vork  furnishes  the  only  proper  basis  for  the  figiire 
work  that  will  follow. 

To  teachers  who  may  find  difficulty  in  supplying  profitable  "  seat- 
work  "  for  their  pupils,  and  who  have  heretofore  kept  them  busy 
with  long  figure-problems,  the  following  is  suggested : 

In  place  of  mere  figure  work,  require  the  pupils  to  copy  certain 
pages  from  this  book,  carefully  filhng  all  the  blanks.     Select  pages 


with  which  the  child  is  quite  familiar,  and  put  the  main  emphasis 
upon  accuracy.  Make  the  lesson  simple  enough,  and  so  impress  the 
pupils  with  the  importance  of  absolute  accuracy  that  at  least  75% 
of  all  the  papers  (or  slates)  examined  will  be  free  from  errors — in 
spelling,  in  use  of  capital  letters,  in  punctuation,  or  in  figures. 
Commend  only  those  who  have  "perfect  papers"  —  perfect  in  respect 
to  the  four  points  named  above. 

The  educative  value  of  such  an  exercise  as  this  is  not  to  be  com- 
pared with  mere  figure  manipulation  in  which  "90%  of  accuracy"  is 
accounted  good,  80%  fair,  and  70%  good  enough  to  "pass."  Let 
the  pupils  early  learn  that  in  arithmetic,  at  least,  nothing  short  of 
almost  perfect  accuracy  is  of  any  value  whatever.  Measure  the 
pupils  in  all  the  grades,  not  so  much  by  the  ratio  of  the  number  of 
accurate  answers  to  the  number  of  problems  given,  but  rather  by 
the  amount  of  work  they  are  able  to  do  ivithout  snaking  any  errors. 
Allow  no  pupil  to  leave  any  grade  of  the  school  with  the  impression 
that  in  number-work  "90%  of  accuracy  "  is  good. 

r.  H.  H. 

Jacksoxville,  III.,  Jan.  1,  1901. 


THE  PRIMER  OF  ARITHMETIC. 


one 


two 
three 

four 
four 
three 


I  I 

n 
III 

II  11 


2 


•   •   • 
3 


4 


inch 


inches 


1  and  1  are 

2  and  1  are 

2  and  2  are 

3  and  1  are 


2  inches  and  1  incli  are 


inches. 
—  inches. 


2  inches  and  2  inches  are  - 
4  inches  less  1  inch  are inches. 

4  inches  less  2  inches  are inches. 

3  inches  less  1  inch  are inches. 

1.  One  half  of  4  inches  is inclies. 

2.  One  half  of  3  inches  is 

3.  One  half  of  2  inches  is inch. 


4.  John  had  a  pencil  exactly  4  inches  long.  He 
broke  it  into  two  equal  pieces.  Each  piece  was 
inches  long. 


A  1-incli  square. 


A  2-incli  fiqnaro. 


1  in.  by  1  in. 


1.  A  square  has 
-  corners. 


2.  A  square  has 
square  comers. 

3.  A  square  has 


2  i'-iclies  by  2  iucLtiB. 


-  equal  sides. 

4.  The  red  s(|uare  is  a square. 

5.  The  yellow  square  is  a square. 


times  as  large  as 
—  as  large  as  the 


6.  The  yellow  square  is  - 
the  red  square. 

7.  The  red  square  is  

yellow  square. 

8.  A  2-inch  square  equals 1-inch  squares. 

9.  A  1-inch  square  equals  what  part  of  a  2-inch 
square  ? 

10.  Two  1-inch  squares  equal  what  part  of  a  2- 
inch  square? 


1.  John  had  3  cents.     His  father  gave  him  1 
cent  more.     He  then  had cents. 

2.  Mary  had  3  cents.     She  spent  1  cent.     She 
then  had cents. 


3.  At  2  cents  each,  two  lemons  cost 
2  times  2  cents  are cents. 


cents. 


4.  How  many  2-cent  stamps  can  you  buy  with  4 
cents  ? 

5.  One  half  of  4  cents*  is cents. 


6.  One  half  of  4  apples  is  - 

7.  One  half  of  3  apples  is  - 

8.  One  half  of  2  apples  is  - 

9.  Two  apples  are  1  half  of 
10.  One  api:)le  is  1  half  of  — 


apples. 


-  apple. 

—  apples, 
apples. 

11.  One  and  one  half  apples  are  one  half  of 

apples. 

12.  Henry  sold  apples  at  the  rate  of  2  apples  for 
1  cent.     For  4  apples  he  should  receive cents. 

3  and  1  =  4  less  2  = 

2  and  1  =  4  less  3  = 

2  and  2  =  4  less  1  = 


-11!!  I 
II 


five 


live 


4  and  1  are . 

3  and are  5. 


5  less  1  = 
5  less  2  = 

1  half  of  5  is 


5  less  4  = 
5  less  3  = 


2  twos  and  1  are 

2  books  and  2  books  are 

3  boys  and  2  boys  are  — 
2  men  and  1  man  are  — 
1  girl  and  4  girls  are  — 


books. 


-  boys, 
men. 
girls. 


2  apples  and  2  apples  are apples. 

4  marbles  and  1  marble  are marbles. 


4  inches  and  1  inch  = 

5  inches  less  2  inches  = 
3  inches  less  2  inches  = 

2  inches  and  3  inches  = 
5  inches  less  3  inches  = 

3  inches  and  2  inches  = 
5  inches  less  1  inch  = 


1.  One  half  of  5  inches  is 


2.  Two  inches  are  1  half  of inches. 

3.  One  and  1  half  inches  are  1  half  of 

inches. 

4.  Two  and  1  half  inches  are  1  half  of 

inches. 

5.  One  inch  is  1  half  of inches. 

6.  In  1  inch  there  are half-inches. 

7.  In  2  inches  there  are half-inches. 

8.  In  2  and  I  half  inches  there  are  

half-inches. 

9.  Henry  had  a  pencil  exactly  5  inches 
long.  He  broke  it  into  two  equal  pieces. 
Each  piece  was inches  long. 


An  oblong. 


7 

An  oblong. 


An  oblong. 


1  in.  by  2  in. 


1. 

has 


An  oblong 
—  corners. 


2.    An  oblong 


lias 


sides. 


1  in.  by  3  in. 


3.  Two  of  the  sides  of  an  ob- 
long are  longer  than  the  other 
two  sides. 

4.  The  red  oblong  is  inch 

wide  and inches  long. 

5.  The    yellow   oblong   is  ^ 

incli  wide  and ■  inches  long. 

6.  How  long  is  the  bine  oblong? 


1  in.  by  5  in. 


8 

1.  Hemy  had  3  cents.     He  earned  2  cents  more. 
He  then  had cents. 

2.  Helen  had  5  cents.     She  spent  3  cents.     She 
then  had cents. 

3.  At  1   cent   each,    5    apples   cost   cents. 

5  times  1  cent  are cents. 

4.  How  many  2-cent  stamps  can  yon  buy  with  5 
cents? 

5.  One  half  of  5  pies  is pies. 


6.  An  oblong  1  inch  wide  and  5  inches  long  is 
equal  to 1-incli  squares. 

7.  An  oblong  1  inch  by  5  inches  is times  as 

large  as  a  1-inch  square. 

8.  Cut  from  paper  a  2-incli  square. 

(a)  Place  it  upon  your  desk  with  one  edge  par- 
allel with  the  front  edge  of  your  desk. 

(b)  Fold   the   front   edge  upon  the  back   edge. 
Crease.     Unfold. 

(c)  Fold   the   right   edge   upon    the    left    edge. 
Crease.     Unfold. 

(d)  A  2-inch  square  is  equal  to 1-inch  squares. 


SIX 


SIX 


SIX 


III 
III 

II  11 


I  I 
II 


5  and  1  are . 

4  and are  6. 

3  and are  6. 


6  less  5  = 
6  less  4  = 


6  less  2 
6  less  3 


4  books  and  2  books  are 

2  hats  and  3  liats  are  — 

3  cows  and  3  cows  are  — 

5  birds  and  1  bird  are  — 
2  flaos  and  3  fla2:s  are  — 


book^ 


hats. 

-  cows. 

-  birds. 
^ . ^.. flass. 

4  sleds  and  2  sleds  are sleds. 


3  twos  = 


C-l 


2  threes  = 


10 


V  1  M  M  '  \,M  '  \-n:y 


i.i.l.Tii,i,i,T,\,\,\ 


3  inches  and  3  inches  = 
6  inches  less  3  inches  = 

4  inches  and  2  inches  = 
^  6  inches  less  2  inches  = 

5  inches  and  1  inch  = 

1.  A  foot  is  twelve  inches. 

2.  One  half  of  a  foot  is inches. 

3.  One  half  of  six  inches  is inches. 

4.  Six  inches  are  one  half  of . 


5.  Three  inches  are  one  half  of . 

6.  In  three  inches  there  are half-inches. 

7.  My  pencil  is  about inches  long. 

8.  My  slate  is  about inches  wide. 

9.  Draw  a  horizontal  line  3  inches  long. 
10.  Draw  a  vertical  line  3  inches  long. 


11 


1.  The  red  oblong  is 

2.  The  red  oblon.s;  is 


inches  wide, 
inches  hins;. 


3.  An  oblong  two  inches  wide  and  3  inches  long 
is  equal  to 1-inch  squares. 

4.  Two  threes  are -.       Three  twos  are . 

5.  An  oblong  1  inch  wide  and  6  inches  long  is 
equal  to 1-inch  squares. 

6.  The  red  oblong  is  how  many  1-inch  squares 
larger  than  a  2-inch  square? 

7.  The  red  oblong  is  how  many  times  as  large  as 
a  1-inch  square? 

8.  One  half  of  the  red  oblong  equals  how  many 
1-inch  squares? 


12 

1.  James  had  4  arrows.     He  made  2  more.     He 
then  had arrows. 

2.  Kichard  had  6  arrows.     He  lost  4  of  them. 
He  then  had arrows. 

3.  At  2  cents  each,  3  oranges  cost  cents. 

3  times  2  cents  are cents. 

4.  How  many  2-cent  stamps  can  you  buy  with  6 
cents?     2  cents  are  contained  in  6  cents times. 

5.  One  half  of  6  days  is days. 


6.  Cut  from  paper  an  oblong  2  inches  by  3  inches. 
Cut  from  paper  a  2-inch  square.  The  oblong  is 
times  as  large  as  the  square. 

7.  Cut  from  paper  6  1-inch  squares. 

(a)  Arrange  these  into  an  oblong  1  inch  by  6 
inches. 

(b)  Arrange  them  into  an  oblong  2  inches  by  3 
inches. 

(c)  Make  with  them  a  2-incli  square.  What  part 
of  a  2-inch  square  can  you  make  with  what  remain? 

8.  Two  1-inch  squares  are of  a  2-inch 

square. 

C-4 


13 


seven 


seven 


seven 


seven 


o    • 


G     ® 


•     • 


9     •     • 


6  and  1  are . 

5  and are  7. 

4  and are  7. 


7  less  1  = 
7  less  2  = 
7  less  3  = 

1  half  of  7  is 

5  pins  and  2  pins  are 
4  caps  and  2  caps  are 
4  hens  and  3  hens  are 
3  eggs  and  3  eggs  are 


D-l 


7  less  6  = 
7  less  5  = 
7  less  4  = 


pins, 
caps, 
hens. 

eggs. 


14 

4  inches  and  3  inches  = 
7  inches  less  3  inches  = 

5  inches  and  2  inches  = 
7  inches  less  2  inches  = 
4  inches  and  3  inches  = 
7  inches  less  4  inches  = 

6  inches  and  1  inch  = 

7  inches  less  1  inch  = 

1.  One  half  of  a  foot  and  1  inch  are inches, 

2.  One  half  of  a  foot  less  1  inch  equals  

inches. 

3.  One  half  of  7  inches  is inches. 

4.  In  three  and  1  half  inches  there  are half- 
inches. 

5.  Three  and  1  half  inches  are  1  half  of  

inches. 

6.  Draw  a  horizontal  line  6  inches  long.  With- 
out measuring,  divide  it  into  two  equal  parts.  Each 
part  should  be inches  long. 

7.  Draw  a  horizontal  line  5  inches  long.  With- 
out measuring,  divide  it  into  two  equal  parts.  Each 
part  should  be inches  long. 


15 


1.  The  yellow  oblong  is  inches  Avide   and 

inches    long.      It   contains   1-inch 


sqnares  and  2  halves  of  a  1-inch  square.  We  say 
that  it  contains  7  square  inches;  that  is,  it  is  7 
times  as  large  as  a  1-inch  square. 

2.  An  oblong  2  inches  by  3  inches  contains 

square  inches. 

3.  A  2-inch  square  contains square  inches. 

4.  Think  of  an  oblong  2  inches  wide  and  2  and 
1  half  inches  long.  How  many  square  inches  does 
it  contain? 

5.  Two  times  3  and  1  half  are . 

6.  Two  times  2  and  1  half  are . 


16 

1.  Mr.  Smith  had  4  cows.     He  bonglit  3  more. 
He  then  had cows. 

2.  Mr.  Harris  had  7  cows.     He  sold  2  of  them. 
He  then  had cows. 

3.  At  2  dollars  each,  3  sheep  cost dollars. 

3  times  2  dollars  are  — -  dollars. 

4.  How  many  2-cent  stamps  can  you  buy  with 
7  cents? 

5.  One  half  of  7  dollars  is dollars. 


6.  An  oblong  1  inch  by  7  inches  contains 

square  inches ;  that  is,  it  is times  as  large  as  a 

1-inch  square. 

7.  In  a  week  there  are days. 

8.  The  first  day  of  the  week  is . 

9.  The  7th  dav  of  the  week  is . 


10.  The  second  day  of  the  week  is . 

11.  George  goes  to  school  5  days  of  each  week, 
and  is  at  home  the  other  days  of  the  week.     He  is 

at  home days.    In  2  weeks  he  is  in  school 

days. 

IM 


17 


eight 

•  •   • 
• 

•  •   • 

• 

8 

eight 

•   •   • 
®   •   • 

•   • 

8 

eight 

o 

•   •   • 

8 

eight 

•  • 

•  • 

8 

7  and  1 

are . 

6  and  — 

—  are  8. 

5  and  — 
4  and  — 

—  are  8. 

—  are  8. 

8  less  4  are . 

8  less  1  =  8  less  7  = 

8  less  2  =  8  less  6  = 

8  less  3  =  8  less  5  = 

1  half  of  8  is . 

5  cents  and  3  cents  are cents. 

4  days  and  3  days  are days. 

6  nails  and  2  nails  are nails. 


4  twos 


9    •    a    • 
•    •    •    • 

E-l 


2  fours  = 


18 

4  inches  and  4  inches  = 
8  inches  less  4  inches  = 

5  inches  and  3  inches  = 
8  inches  less  3  inches  = 

6  inches  and  2  inches  = 
8  inches  less  2  inches  = 
8  inches  less  6  inches  = 

1.  One  half  of  a  foot  and  2  inches  are inches. 

2.  One  half  of  a  foot  less  2  inches  equals 

inches. 

3.  One  half  of  8  inches  is inches. 

4.  In  4  inches  there  are half-inches. 

5.  Four  inches  are  1  half  of inches. 

6.  Draw  a  horizontal  line  7  inches  long.  With- 
out measuring,  divide  it  into  two  equal  parts.  Each 
part  should  be inches  long. 

7.  Draw  a  horizontal  line  8  inches  long.  With- 
out measuring,  divide  it  into  two  equal  parts.  Each 
part  should  be inches  long. 

8.  Draw  a  vertical  line  4  inches  long.  Without 
measuring,  divide  it  into  two  equal  parts.  Each 
part  should  be inches  long. 


19 


1.  The  green  oblong  is  — 
inches  long.     In  it  there  are 


inches  wide  and 


1-inch  squares. 


2.  An  oblong  2  inches  by  4  inches  contains 

square  inches;  that  is,  it  is times  as  large  as 

a  1-inch  square. 

3.  Two  times  4  are . 

4.  Four  times  2  are . 

5.  Three  times  2  are . 

6.  Two  times  2  are . 


7.  Two  times  2  cents  are cents. 

8.  Three  times  2  cents  are cents. 

9.  Four  times  2  cents  are cents. 

10.  Two  times  3  cents  are cents. 


20 

1.  Mrs.   Smith    had   5   boxes   of    berries.      She 
picked  3  boxes  more.     She  then  had boxes. 

2.  Mrs.  Harris  had  8  boxes  of  berries.     She  sohl 
6  box-es.     She  then  had boxes. 

3.  Mary  gets  2  cents  a  box  for  picking  berries. 

For  picking  4  boxes  she  gets cents.     4  times  2 

cents  are cents. 

4.  How  many  2-cent  stamps  can  you  buy  for  8 
cents?    2  cents  are  contained  in  8  cents times. 

5.  One  half  of  8  boxes  of  berries  is boxes  of 

berries.  

6.  An  oblons;  1  inch  by  8  inches  contains 


square  inches ;  that  is,  it  is times  as  large  as  a 

1-inch  square.  

7.  Cut  from  paper  an  oblong  2  inches  by  4  inches. 

(a)  Place  it  on  your  desk  with  the  long  edge  par- 
allel with  the  front  edge  of  your  desk. 

(b)  Fold    the   right   edge   upon   the    left   edge. 
Crease.     Unfold. 

(c)  Observe,  that  an  oblong  2  inches  by  4  inches 
is  equal  to  two squares. 


21 


nine 


nine 


nine 


nine 


•   •    • 


8  and  1  are 


7  and 
6  and 
5  and 
9  less  2  = 
9  less  3  = 
9  less  4  = 


are  9. 

are  9. 

are  9. 

9  less  7  = 
9  less  6  = 
9  less  5  = 


1  half  of  9  is 


3  threes  = 


•    • 
e    • 

F-l 


1  third  of  9  = 


22 

5  inches  and  4  inches  = 
9  inches  less  4  inches  = 

6  inches  and  3  inches  = 

6  inches  less  3  inches  = 

7  inches  and  2  inches  = 
7  inches  less  2  inches  = 

1.  One  half  of  a  foot  and  3  inches  are  

inches. 

2.  One  half  of  a  foot  less  3  inches  equals  '■ 

inches. 

3.  One  half  of  9  inches  is inches. 

4.  One  third  of  9  inches  is inches. 

5.  Two  thirds  of  9  inches  are inches. 

6.  Draw  a  horizontal  line  9  inches  long.  Divide 
it  into  two  equal  parts.  Each  part  should  be 
inches  long. 

7.  Draw  a  horizontal  line  9  inches  long.     Divide 

it  into  three  equal  parts.     Each  part  should  be 

inches  long. 

8.  Draw  a  vertical  line  6  inches  long.     Divide 

it  into  three  equal  parts.    Each  part  should  be 

inches  long. 


23 


1.  The  blue  ligure  is  a square.     In  it  there 

are 1-inch  squares. 

.2.  A  3-inch  square  contains  square  inches; 

that  is,  it  is  ■ times  as  large  as  a  1-inch  square. 

3.  Three  times  2  are . 

4.  Three  times  3  are . 

5.  Two  times  3  marks  are  - 


6.  Three  times  3  marks  are 

7.  Two  times  4  marks  are  - 

8.  Four  times  2  marks  are  - 

F-a 


marks. 
-  marks. 


marks, 
marks. 


24 

1.  Jane  paid  5  cents  for  a  tablet  and  4  cents  for 
a  pencil.     For  both  she  paid cents. 

2.  Lily  is  9  years  old  and  her  sister  is  6  years  old. 
Lily  is years  older  than  her  sister. 

3.  At  3  cents  each,  2  oranges  cost cents;  3 

oranges  cost cents. 

2  times  3  cents  are cents. 

3  times  3  cents  are cents. 

4.  How  many  3-cent  stamps  can  you  buy  for  9 
cents?     3  cents  are  contained  in  9  cents times. 

5.  One  third  of  9  days  is days. 

6.  Two  thirds  of  9  days  are days. 


7.  Look  at  the  figure  on  page  19.     If  this  figure 

were  1  inch  longer  than  it  is,  it  would  contain 

square  inches.  An  oblong  2  inches  by  4  and  1  half 
inches  contains square  inches. 

4i  and  4i  are  — 

2  times  4i  are  — 

3i  and  3^  are  — 

2  times  3i  are  — 

2  times  2i  are  — 


25 


ten 

ten 
ten 
ten 
ten 


•   • 


•   •    • 


9  and  1  are 


8  and 
7  and 
6  and 
5  and 
10  less  2  = 
10  less  3  = 
10  less  6  = 

ten 


10 

10 
10 
10 
10 


are  10. 

are  10. 

are  10. 

are  10. 
10  less  8 
10  less  7 
10  less  4 


10 


26 

5  inches  and  5  inches  = 
10  inches  less  5  inches  = 

6  inches  and  4  inches  = 

6  inches  less  4  inches  = 

7  inches  and  3  inches  = 
7  inches  less  3  inches  = 

1.  One   half   of   a   foot   and   4  inches  are 
inches. 

2.  One  half  of  a  foot  less  4  inches  equals 
inches. 

3.  One  half  of  10  inches  is inches. 

4.  In  5  inches  there  are half-inches. 

5.  Five  inches  are  1  half  of inches. 


j  One  half  of  4  inches  is  — 
(  Four  inches  are  1  half  of 
( One  half  of  3  inches  is  — 


8. 


9. 


nches. 
-  inches. 


( Three  inches  are  1  half  of inches. 

One  half  of  2  inches  is inch. 

Two  inches  are  1  half  of inches. . 

One  half  of  5  inches  is . 

Five  inches  are  1  half  of inches. 


27 


1.  The  yellow  figure 
is    an    oblong.      It    is 

inches    wide    and 

inches  long.     In  it 


are I-inch  squares. 

2.  An  oblong  2  inches 
by   5   inches  contains 

square  inches;  that 

is,   it  is  times  as 

large  as  a  1-inch  square. 

3.  Two  times  five  1- 

inch    squares    are   

1-inch  squares. 

4.  Five  times  two  1- 

inch    squares    are   

1-inch  squares. 

5.  Two    times    five 
books  are books. 

6.  Five    times    two 
books  are books. 

7.  Two  times  5  = 

8.  Five  times  2  = 


28 

1.  Alice  is  8  years  old.     In  two  years  more  she 
will  be years  old. 

2.  Susie  is  10  years  old.     She  began  to  go  to 
school  4  years  ago.     Then  she  was years  old. 

3.  At  5  cents  each,  2  pencils  cost cents. 

2  times  5  cents  are cents. 

4.  How  many  2-cent  stamps  can  you  buy  for  10 
cents?    2  cents  are  contained  in  10  cents times. 

5.  One  third  of  9  years  is years. 


^     (One  third  of  3  inches  is inch. 

6.  < 

( Three  inches  are  1  third  of inches. 


7.  Look  at  the  figure  on  page  19.     If  this  figure 

were  1  inch  shorter  than  it  is,  it  would  contain 

square  inches.  An  oblong  2  inches  by  2A  inches 
contains square  inches.     2i  and  2h  are . 

2  times  2h  are . 

2  times  3i  are . 

2  times  li  are . 

2h  and  2h  and  2i  = 

3  times  2h  are . 

G-4 


29 


eleven 


10  and  1  are 


9  and  - 
8  and  - 
7  and  - 
6  and  - 

11  less  1  = 

11  less  2  = 

11  less  3  = 

11  less  4  = 

11  less  5  = 

One  half  of  11  is 


11 


are  11. 
are  11. 
are  11. 
are  11. 
1  less  10  = 


1  less 
1  less 
1  less 
1  less 


9  = 

8  = 
7  = 
G  = 


8  chairs  and  3  chairs  are 
5  chairs  and  1  chairs  are 
7  chairs  and  4  chairs  are 


chairs, 
chairs, 
chairs. 


4  flags  and  6  flags  are 
6  flags  and  5  flags  are 
8  flags  and  2  flags  are 


flags, 
flags, 
flags. 


30 

6  inches  and  5  inches  = 
11  inches  less  6  inches  = 

7  inches  and  4  inches  = 

7  inches  less  4  inches  = 

8  inches  and  3  inches  — 
8  inches  less  3  inches  = 

1.  One  half  of  a  foot  and  5  inches  are inches. 

2.  One  half  of  a  foot  less  5  inches  eqnals 

inch. 

3.  One  half  of  11  inches  is inches. 

4.  In  51  inches  there  are half-inches. 

5.  Five  and  1  half  inches  are  1  half  of  

inches. 

6.  My  book  is  abont inches  wide. 

7.  My  book  is  about inches  long. 

8.  My  pencil  is  about inches  long. 


9.  Draw  two  parallel  vertical  lines  one  half-inch 
apart  and  4  inches  long. 

10.  Draw  two  parallel  horizontal  lines  one  half- 
inch  apart  and  4  inches  long. 


31 


1.  An  oblong  2  inclies  wide  and  5h  inches  long 

contains square  inches. 

5h  and  5h  are . 

Two  times  5h  are . 


2.  Which   is  the   larger,  a  3-inch   s(|Liare   or  an 
oblong  2  inches  by  5  inches? 

The  square  contains sc^uare  inches. 

The  oblong  contains square  inches. 

3.  Which   is  the   larger,   a  2-inch   square   or  an 
oblong  1  inch  by  5  inches? 

The  square  contains square  inches. 

The  oblong  contains square  inches. 

4.  How  many  square  inches  in  an  oblong  that  is 
half  a  foot  long  and  1  inch  wide  ? 

5.  I  am  thinking  of  an  oblong  that  is  2  inches 
wide.    It  contains  6  square  inches.    How  long  is  it? 

2  times are  6. 

6.  I  am  thinking  of  an  oblong  that  is  2  inches 
wide.    It  contains  8  square  inches.    How  long  is  it? 

2  times are  8. 

2  times are  5. 

2  times are  7. 


32 

1.  Jason  rode  on  his  wheel  6  miles  Monday  and 
5  miles  Tuesday.     In  all  he  rode miles. 

2.  Little  Joe  started  in  the  morning  to  ride  to 
his  uncle's  home,  11  miles  away.  By  noon  he  had 
ridden  7  miles.     He  had miles  farther  to  go. 

3.  Bennie  can  easily  ride  his  wheel  at  the  rate  of 
5  miles  an  hour.     In  2  hours  he  can  ride miles. 

2  times  5  miles  are miles. 

4.  How  many  5-cent  stamps  can  you  buy  with 
11  cents? 

5.  One  third  of  9  miles  is miles. 


6.  There  are  5  school  days  in  a  week.     In  two 
weeks  there  are school  days. 

7.  Frank  had  6  cents  and  his  brother  had  half 
as  many.     Together  they  had cents. 

8.  Two  yards  of  ribbon  at  4  cents  a  yard  will 
cost cents. 

9.  A  nickel  is cents. 

10.  A  dime  is cents. 

11.  A  nickel  and  a  dime  are cents. 

12.  A  "quarter"  is cents. 


33 


twelve 


12 


1^^ 


11  and  1  are 


10  and 
9  and 
8  and 
7  and 
12  less  2  = 
12  less  3  = 
12  less  4  = 
12  less  5  = 
12  less  6  = 


are  12. 

are  12. 

are  12. 

are  12. 
12  less  10 
12  less  9 
12  less  8 
12  less  7 
2  sixes  = 


One  lialf  of  12  is 


9  books  and  3  books  are books. 

8  books  and  2  books  are books. 

7  books  and  5  books  are books. 


5  girls  and  6  girls  are 
4  girls  and  8  girls  are 
3  girls  and  7  girls  are 


girls, 
girls, 
girls. 


34 

6  inches  and  6  inches  = 
12  inches  are  1 . 

1  foot  less  5  inches  = 
1  foot  less  4  inches  = 

7  inches  and  5  inches  = 
1  foot  less  3  inches  = 

8  inches  and  4  inches  = 

8  inches  are  1  fourth  of  a  foot. 
6  inches  are of  a  foot. 

9  inches  are of  a  foot. 

i  of  a  foot  and  1  inch  are inches. 

i  of  a  foot  and  1  inch  are inches. 

f  of  a  foot  and  1  inch  are inches. 

f  of  a  foot  less  1  inch  are inches. 


1.  Draw  on  the  blackboard  two  parallel  horizon- 
tal lines  1  foot  long  and  2  inches  apart. 

2.  Draw  a  1-foot  square.  Draw  a  2-foot  square. 
The  2-foot  square  is  how  many  times  as  large  as  the 
1-foot  square? 

3.  Draw  an  oblong  1  foot  wide  and  3  feet  long. 
The  oblong  is  equal  to 1-foot  squares. 


35 

1.  An  oblong  2  inches  wide  and  6  inches  long 

contains square  inches. 

6  and  6  are . 

Two  times  6  are . 

Six  times  2  are . 


2.  Which  is  the  larger,   a  2-foot   square  or  an 
oblong  that  is  1  foot  by  5  feet? 

The  square  contains square  feet. 

The  oblong  contains square  feet. 

3.  Wliicli  is  the  larger,   a  3-foot   square  or  an 
oblong  2  feet  by  5  feet? 

The  square  contains square  feet. 

The  oblong  contains square  feet. 

4.  How  many  square  inches  in  an  oblong  that  is 
half  a  foot  long  and  2  inches  wide? 

5.  I  am  thinking  of  an  oblong  that  is  2  inches 
wide.    It  contains  10  square  inches.    How  long  is  it? 

2  times are  10. 

6.  1  am  thinking  of  an  oblong  that  is  2  inches 
wide.    It  contains  12  square  inches.    How  long  is  it? 

2  times are  12. 

6  times are  12. 


36 

1.  Herbert  worked  7  hours  Monday  and  5  liours 
Tuesday.     In  both  days  he  Avorked hours. 

2.  Mr.  Jones  works  12  hours  each  day.     His  son 

works  8  hours.     The  father  works hours  more 

than  the  son. 

3.  Alfred  worked  2  hours  a  day  for  all  the  work- 
ing days  of  a  week.     In  all  he  worked hours. 

6  times  2  hours  are hours. 

4.  Wilbur  can  cane  a  chair  in  2  hours.     In  10 
hours  he  can  cane chairs. 

2  hours  are  contained  in  10  hours times. 

5.  One  third  of  6  hours  is hours. 


6.  There  are  6  working  days  in  a  week.     In  2 
weeks  there  are working  days. 

7.  Peter  had  8  cents  and  his  brother  had  half  as 
many.     Together  they  had cents. 

8.  Two  yards  of  ribbon  at  6  cents  a  yard  will 
cost cents. 

9.  A  year  is  12  months. 

One  fourth  of  a  year  is months. 

Three  fourths  of  a  year  are months. 


37 

3  fours  =  4  threes  = 

2  fours  =  3  threes  = 

1.  Four  times  3  stars  are stars. 

2.  Three  times  4  stars  are stars. 

3.  One  third  of  12  stars  is stars. 

4.  Two  thirds  of  12  stars  are stars. 

5.  Four  stars  are of  12  stars. 

6.  Six  stars  are  —  of  12  stars. 

7.  Three  stars  are of  12  stars. 


9  stars  and  3  stars  are stars. 

8  stars  and  4  stars  are stars. 

12  stars  less  3  stars  are stars. 

12  stars  less  4  stars  are stars. 

6  stars  and  6  stars  are stars. 

12  stars  less  5  stars  are stars. 

12  stars  less  2  stars  are stars. 

12  stars  less  6  stars  are stars. 


38 

1.  Draw  a  line  on  the  blackboard  3  feet  long. 

Three  feet  are  1  yard. 

2.  Draw  a  line  on  the  blackboard  2  yards  long. 

Two  yards  are feet. 

3.  Measure  off  three  yards  of  string.  , 

Three  yards  are feet. 

4.  Measure  off  four  yards  of  string. 

Four  yards  are feet. 

5.  One  yard  is feet.     One  half  of  a  yard 

is' feet. 

6.  One  third  of  a  yard  is foot. 

7.  Two  thirds  of  a  yard  are feet. 

8.  One  and  1  third  yards  are feet. 

9.  One  and  2  thirds  yards  are feet. 

10.  One  and  1  half  yards  are feet. 

11.  Draw  a  1-foot  square.  Draw  a  3-foot  square. 
The  3-foot  square  is  how  many  times  as  large  as  the 
1-foot  square? 

12.  Which  is  the  larger,  a  1-yard  square  or  a 
3-foot  square? 

13.  Draw  a  line  one  yard  long.  Divide  it  into  2 
equal  parts.    Each  part  should  be long. 


39 


1.  This  oblong  is 
long.     It  contains  - 


-  inches  wide  and 
square  inches. 


inches 


4  threes  are 
3  fours  are  - 
2  sixes  are  - 


2.  I  am  thinking  of  a  1-yard  square  divided  into 
1-foot  squares.     How  many  rows  of  1-foot  squares? 
How  many  1-foot  squares  in  each  row? 
3  threes  are . 


40 

1.  Albert  had  6  liens.     He  bought  5  more.     He 
then  had hens. 

2.  Hattie  had  10  hens.    She  sold  6  of  them.    She 
then  had hens. 

3.  A  horse  needs  4  shoes.      Three  horses  need 

. shoes. 

3  times  4  shoes  are shoes. 

4.  Hiram  earns  4  cents  an  hour.     In  how  many 
hours  can  he  earn  12  cents? 

4  cents  are  contained  in  12  cents times. 

5.  One  third  of  12  cents  is cents. 


6.  Buttons,  eggs,  oranges,  lemons,  etc.,  are  often 
bought  by  the  dozen.     A  dozen  is  12. 

7.  Men  sometimes  count  eggs  by  taking  3  eggs  in 
each  hand. 

3  eggs  and  3  eggs  are eggs. 

6  eggs  and  6  eggs  are eggs. 

One  six  is  half  a  dozen. 

Two  sixes  are dozen. 

Four  sixes  are dozen. 

3.  Two  dozen  eggs  are sixes  of  eggs. 


41 

EEYIEW   OF   Xr:\IBER   FACTS. 

Read  first  by  column ;  tlieii  by  line. 


3  +  2  = 

2 

twos  = 

5-2  = 

5-3: 

4  +  2  = 

3  twos  = 

6-2  = 

6-4: 

4  +  3  = 

4 

twos  = 

7-3  = 

7-4: 

5  +  2  = 

5  twos  = 

7-2  = 

7-5: 

5  +  3  = 

6 

twos  = 

8-3  = 

8-5: 

6  +  2  = 

2  threes  = 

8-2  = 

8-6: 

5  +  4  = 

3  threes  = 

9-4  = 

9-5 

6  +  3  = 

4 

threes  = 

9-3  = 

9-6 

7  +  2  = 

2 

fours  = 

9-2  = 

9-7 

6  +  4  = 

3 

fours  = 

10-4  = 

10-6 

7  +  3  = 

2 

fives  = 

10  -  3  = 

10-7 

8  +  2  = 

2 

sixes  = 

10-2  = 

10-8 

6  +  5  = 

i 

of  2  = 

11-5  = 

11-6 

7  +  4  = 

i 

of  3  = 

11-4  = 

11-7 

8  +  3  = 

i 

of  4  = 

11-3  = 

11-8 

9  +  2  = 

i 

of  5  = 

11  -  2  = 

.      11  -  9 

7  +  5  = 

i 

of  6  = 

12-5  = 

12-7 

8  +  4  = 

^ 

of  7  = 

12-4  = 

12-8 

9  +  3  = 

i 

of  8  = 

12-3  = 

12-9 

i  of  9  = 

i 

of  10  = 

i  of  11  = 

i  of  12 

^  of  6  = 

i 

of  9  = 

f  of  9  = 

i  of  12 

1  of  12  = 

i 

of  8  = 

i  of  12  = 

1  of  12 

12  inclies  are  1  foot.  3  feet  are  1  yard. 

1  week  is  7  days.  1  year  is  12  months. 

1  dozen  is  12  ones. 


42 

1.  This  room  is  about yards  wide  and  about 

■ yards  long. 

2.  This  room  is  about yards  high. 

3.  The  door  is  more  than yards  high.    Is  it 

more  or  less  than  1  yard  wide  ? 

4.  The  teacher's  desk  is  feet  inches 

long.     It  is feet inches  high.     IIow  wide 

is  it? 

5.  Kuby  is feet  — -  inches  tall. 


6.  One  half  of  2  feet  is foot. 

7.  Two  feet  are  1  half  of feet. 

8.  One  half  of  4  feet  is feet. 

9.  Fouf  feet  are  1  half  of feet. 

10.  One  half  of  6  feet  is feet. 

11.  Six  feet  are  1  half  of feet. 

12.  Adam  is  3  feet  8  inches  tall.    Oscar  is  3  feet 

4  inches   tall.     Adam   is  inches  taller  than 

Oscar. 

13.  Abbie  is  3  feet  9  inches  tall.     Sarah  is  3 
inches  taller  than  Abbie.     Sarah  is tall. 

14.  Four  feet  and  1  foot  2  inches  are . 


43 


1.  The  above  figure  is  inclies  long.     It  is 

—  inches  wide. 


2.  The  perimeter  of  a  figure  is  the  distance  around 
it.    The  perimeter  of  the  above  .oblong  is inches. 

3.  The  area  of   a   figure    is  the  amount   of   its 

surface.     The    area   of   the    above    oblong   is  

square  inches. 

4.  The    perimeter    of   a   2-inch    square    is  

inches. 

5.  The  area  of  a  2-inch   square   is  square 

inches. 

6.  Draw  an  oblong  and  tell  its  perimeter  and  its 
area. 


44 

1.  William  had  7  slieep.     He  bought  5  more. 
He  then  had sheep. 

2.  Elsie  had  12  chickens.     The  rain  killed  5  of 
them.     She  then  had chickens. 

3.  At  6  cents  each,  2  melons  cost cents. 

2  times  6  cents  are cents. 

4.  Ernest  earns  6  cents  an  liom\     In  how  many 
hours  can  he  earn  12  cents? 

6j^  are  contained  in  12^ times. 

5.  Dora  paid  12  cents  for  three  lemons.     One 
lemon  cost cents. 

One  third  of  12  cents  is cents. 


6.  At  6^  a  dozen,  2  dozen  buttons  cost  

cents.     Half  a  dozen  cost cents. 

7.  Six  eggs  and  6  eggs  and  6  eggs  and  6  eggs 
make dozen  eggs. 

8.  Six  inches  and  6  inches  and  6  inches  and  6 
inches  make feet. 

9.  Six  months  and  6  months  and  6  months  and 
6  months  make years. 

10.  Three  eggs  are of  a  dozen. 


45 


twenty 


20 


thirty 


30 


2  tens  and  1  are . 

3  tens  and  2  are . 

4:  tens  and  3  are  — — . 
5  tens  and  5  are . 

12  3  4  5 

11      12  13  U  15 

21      22  23  24  25 

31      32  33  34  35 

34  is  3  tens  and . 

53  is  5  tens  and . 


2  tens  are . 

3  tens  are  — . 

4  tens  are  forty. 

5  tens  are  fifty. 

.  2  tens  and  5  are 

.  3  tens  and  6  are 

- — .  4  tens  and  4  are 
.              5  tens  and  9  are 


6  7  8  9  10 

16  17  18  19  20 

26  27  28  29  30 

36  37  38  39  40 

46  is  4  tens  and . 

27  is  2  tens  and . 


46 


10  and  1 

are 

10  and  2 

are 

10  and  3 

are 

10  and  4 

are 

10  and  5 

are 

10  and  6 

are 

10  and  7 

are 

10  and  8 

are 

10  and  9 

are 

19  and  1 

are 

20  and  1  are 
20  and  2  are 
20  and  3  are 
20  and  4:  are 
20  and  5  are 
20  and  6  are 
20  and  7  are 
20  and  8  are 
20  and  9  are 
29  and  1  are 


1.  Charlie's  book  cost  25  cents  and  liis  pencil 

cost  2  cents.     Together  they  cost cents. 

25  is tens  and . 

27  is tens  and  — -. 


2.  Thomas  had  34  marbles, 
him  2  more.     He  then  had 


His  brother  gave 
marbles. 


12  +  2  = 

14  +  2  = 
16  +  2  = 

18  +  2  = 


22  +  2 
24  +  2 

26  +  2 
28  +  2 


32  +  2 

34  +  2 
36  +  2 

38  +  2 


47 


A  1-iuch  cube. 


A  2-inch  cube. 


1.  With  1-incli  cubes,  build  a  2-inch  cube.     It 
takes 1-inch  cubes  to  make  a  2-inch  cube. 

2.  A  2-inch  cube  contains cubic  inches ;  that 

is,  it  is times  as  large  as  a  1-inch  cube. 

2  times  2  cubic  inches  are cubic  inches. 

2  times  4  cubic  inches  are cubic  inches. 


48 

1.  Aaron  paid  35  cents  for  a  book  and  3  cents 
for  paper.     For  both  he  paid cents. 

2.  Maggie  had  35  chickens.     A  rat  killed  3  of 
them.     She  then  had chickens. 

3.  A  bntterfly  has wings.    Three  butterflies 

have wings. 

3  times  4  wings  are  — —  wings. 

4.  At  2  cents  each,  how  many  oranges  can  you 
buy  for  10  cents? 

2^  are  contained  in  10^ times. 

5.  Willis  paid  8  cents  for  4  lemons.    One  lemon 
cost cents. 

One  fourth  of  8  cents  is cents. 


6.  Thirteen  eggs  are  1  dozen  and . 

7.  Thirteen  cents  are  1  dime  and cents. 

8.  Thirteen  inches  are  1  foot  and inch. 

9.  Thirteen  months  are  1  year  and month. 

10.  Thirteen  feet  are  4  yards  and foot. 

11.  Three  buttons  are  1  fourth  of  a . 

12.  Three  inches  are  1  fourth  of  a . 

13.  Three  months  are  1  fourth  of  a  — — . 


49 

7  stars  and  7  stars  are stars. 

2  sevens  are .     7  twos  are  — 

2  times  7  stars  are stars. 

7  times  2  stars  are stars. 


1.     One  week  is  days,  and  two  weeks  are 

—  days. 

7  days  and  7  days  are days. 

2  times  7  days  are days. 


Six  tens  are  sixty.     Seven  tens  are  seventy. 
Eight  tens  are  eighty.     Nine  tens  are  ninety 
Ten  tens  are  one  hundred. 

2  tens  and  2  tens  are . 

One  half  of  40  is . 

3  tens  and  3  tens  are . 

One  half  of  60  is . 

4  tens  and  4  tens  are . 

One  half  of  80  is . 


50 


12  and  2  are 
32  and  2  are 
52  and  2  are 
72  and  2  are 

94  less  2  are 
74  less  2  are 
54  less  2  are 
34  less  2  are 
14  less  2  are 


22  and  2  are 
42  and  2  are 
62  and  2  are 
82  and  2  are 


84  less  2  are 
64  less  2  are 
44  less  2  are 
24  less  2  are 
14  less  1  are 


1.  One  half  of  40  =  i  of  6  = 

One  half  of  46  is . 

2.  One  half  of  60  =  i  of  8  = 

One  half  of  68  is . 

3.  One  half  of  80  =  i  of  4  = 

One  half  of  84  is . 

4.  Nancy's  book  cost  40  cents.  Her  sister's  book 
cost  half  as  much.     Together  they  cost cents. 

5.  Julian's  book  cost  30  cents.  His  brother's 
book  cost  twice  as  much.  His  brother's  book  cost 
cents. 


51 


A  1-iucli  cube. 

1.  This  prism  is  1  inch 
wide,  1  inch  thick,  and  4 
inches  long. 

2.  It  is   equal    to  1- 

inch  cubes. 

3.  It  contains  cubic 

inches;    that   is,    it   is  


times   as   large  as  a  1-inch 
cube. 

4.  The  prism  is  equal  to 
what  part  of  a  2-inch  cube? 

5.  One   half    of   a   2-inch 
cube  contains  cubic  inches. 

6.  A  prism  I  inch  by  2  inches  by  4  inches  con- 
tains   cubic  inches. 

M-3 


iiiii'i' iii'iinHHiii niiiHniiiiiii 

A  square  prism. 


52 

1.  Mr.  Davis  had  42  slieep.    He  bought  6  more. 
He  then  had sheep. 

2.  Mr.  Evans  had  59  sheep.     Six  of  them  died. 
He  then  had sheep. 

3.  At  7  cents  a  yard,  2  yards  of  ribbon  cost 

cents. 

2  times  7  cents  are cents. 

4.  HoAv  many  2-cent  stamps  can  you  buy  for  1-1 

cents? 

2^  are  contained  in  14^ times. 

5.  Albert  paid   14  cents   for  2  melons.      One 
melon  cost cents. 

One  half  of  14  cents  is cents. 


6.  Fourteen  eggs  are  1  dozen  and  - 

7.  Fourteen  cents  are  1  dime  and  - 

8.  Fourteen  inches  are  1  foot  and  - 

9.  Fourteen  days  are weeks. 

10.  Fourteen  months  are  1  year  and 

11.  Fourteen  feet  are  4  yards  and  — 

12.  Nine  buttons  are  3  fourths  of  a 

13.  Nine  inches  are  3  fourths  of  a  - 


-  cents. 

-  inches. 

-  months, 
feet. 


53 

5  stars  and  5  stars  and  5  stars  : 
3  and  3  and  3  and  3  and  3  = 

3  times  5  stars  are stars. 

5  times  3  stars  are stars. 


1.  Two  nickels  equal cents. 

2.  Three  nickels  equal cents. 

3.  One  dime  and  1  nickel  ecjual cents. 

4.  Two  dimes  equal cents. 

5.  Two  dimes  and  1  nickel  equal cents. 

6.  Three  dimes  equal cents. 

7.  Three  dimes  and  1  nickel  equal cents. 

8.  Four  dimes  and  1  nickel  equal cents. 

9.  Five  dimes  and  1  nickel  equal cents. 

10.  A  quarter  and  a  nickel  equal cents. 

11.  One  yard  is  feet.     Two  yards  are  — 


feet.     Three  yards  are  feet.     Four  yards  are 

feet.     Five  vards  are feet. 


54 

18  and  2  =  28  and  2  = 

38  and  2  =  48  and  2  = 

58  and  2  =  68  and  2  = 

78  and  2  =  88  and  2  = 


21  less  2  are .  31  less  2  are 

41  less  2  are  - — .  51  less  2  are 

61  less  2  are .  71  less  2  are 

81  less  2  are .  91  less  2  are 

101  less  2  are .  151  less  2  are 


30  =  20  and  10. 

1.  One  half  of  30  is  (1  ten  and  5) . 

50  =  40  and  10. 

2.  One  half  of  50  is  (2  tens  and  5) . 

70  =  60  and  10. 

3.  One  half  of  70  is  (3  tens  and  5) . 

90  =  80  and  10. 

4.  One  half  of  90  is  (4  tens  and  5) . 

5.  Jnlia's  book  cost  50  cents.  Her  brother's 
book  cost  half  as  much.  Her  brother's  book  cost 
cents. 


55 


1.  A  cube  has equal  faces.     In  tliis  picture 

of  a  cube,  three  of  the  faces  can  be  seen  and  

are  hicklen  from  view. 

2.  Each  face   of    a    1-inch   cube   is  a inch 

square. 

3.  Each  face   of    a   2-inch    cube   is   a inch 

square. 

4.  The  area  of  one  face  of  a  2-inch  cube  is 

s(|uare  inches. 

5.  Each  face  of  a  3-inch  cube  is  a . 

6.  A  cube  has corners.     In  this  picture  of  a 

cube,   7   of    the   corners   are   in  sight  and  is 

hidden  from  view. 

7.  A  cube  has edges.     In  this  picture  of  a 

cube,  9  of  tlie  edges  are  in  sight  and are  hidden 

from  view. 

N-3 


56 

1.  There  were    36    pupils   in    a   certain   room. 

Four   more  Avere  sent   in.      Then  there  were  

pupils  in  the  room. 

2.  There    Avere  50   pupils    in    a   certain    room. 

Four  were  sent  out.     Then  there  were  pupils 

in  the  room. 

3.  At  5  cents  a  yard,  3  yards   of   ribbon  cost 
cents. 

3  times  5  cents  are cents. 

4.  How  many  3-cent  stamps  can  you  buy  with 
15  cents? 

3^  are  contained  in  15^ times. 

5.  Oscar  paid  15  cents  for  3  tablets.     One  tab- 
let cost cents. 

One  third  of  15  cents  is cents. 


6.  Fifteen  eggs  are  1  dozen  and . 

7.  Fifteen  cents  are  1  dime  and cents. 

8.  Fifteen  inches  are  1  foot  and inches. 

9.  Fifteen  days  are  2  Aveeks  and day. 

10.  Fifteen  months  are  1  year  and months. 

11.  Fifteen  feet  are yards. 


57 

8  stars  and  8  stars  are stars. 

4:  and  4  and  4  and  4  = 

2  times  8  stars  are stars. 

8  times  2  stars  are stars. 

4  times  4  stars  are stars. 


1.  A   spider   has  legs.     Two   spiders   have 

legs. 

2  times  8  legs  are legs. 

2.  A  dog  has legs.     Four  dogs  have legs. 

4  times  4  legs  are legs. 

3.  A  bird  has  2  legs.     Eight  birds  have legs. 

8  times  2  legs  are legs. 

4.  An  ox  needs  - —  shoes.     Two  oxen  need 

shoes. 

2  times  8  shoes  are shoes. 

5.  A  horse  needs shoes.     Four  horses  need 

shoes. 

4  times  4  shoes  are shoes. 


58 


19  and  2  = 
39  and  2  = 
59  and  2  = 
79  and  2  = 


29  and  2 
49  and  2 
69  and  2 
89  and  2 


22  less  2  are 
45  less  2  are 
67  less  2  are 
89  less  2  are 
102  less  2  are 


33  less  2  are 
54  less  2  are 
73  less  2  are 
98  less  2  are 
152  less  2  are 


26  =  20  and  6. 

1.  One  half  of  26  is  (1  ten  and  3) . 

48  =  40  and  8. 

2.  One  half  of  48  is  (2  tens  and  4) . 

64  =  60  and  4. 

3.  One  half  of  64  is  (3  tens  and  2) . 

82  =  80  and  2. 

4.  One  half  of  82  is  (4  tens  and  1) . 

5.  Jennie's  book  cost  46  cents.  Her  sister's 
book  cost  half  as  much.  Her  sister's  book  cost 
cents. 


Take  a  4-inch  square  of  paper.  Fold  lower  edge  upon  upper  edge. 
Crease.  Unfold.  Fold  lower  edge  to  the  crease.  Crease.  Unfold.  Fold 
upper  edge  to  the  middle  crease.  Crease.  Unfold.  Fold  right  edge  upon 
left  edge.  Crease.  Unfold.  Fold  right  edge  to  the  middle  crease.  Crease. 
Unfold.  Fold  left  edge  to  the  middle  crease.  Crease.  Unfold.  Cut  as 
indicated  by  the  heavy  lines.  Then  fold  into  a  box  2  inches  square,  having 
the  four  squares  in  the  middle  for  the  bottom  of  the  box.  Paste  the  corner 
squares  upon  those  next  to  them.     The  box  will  contain cubic  inches. 


0-3 


60 

1.  There  were   28   pupils   in   a   certain   room. 

Four  more  were  sent  in.      Then  there  were  

pupils  in  the  room. 

2.  There   were  42   pupils    in    a   certain    room. 

Four  were  sent  out.     Then  there  were pupils 

in  the  room. 

3.  There  were  8  pupils  in  each  row  of  seats. 
How  many  in  2  rows? 

2  times  8  pupils  are pupils. 

4.  How  many  4-cent  stamps  can  you  buy  with 

16  cents? 

4^  are  contained  in  16^ times. 

5.  Bernie  paid  16  cents  for  2  boxes  of  berries. 
One  box  of  berries  cost cents. 

One  half  of  16  cents  is cents. 


6.  Sixteen  eggs  are  1  dozen  and . 

7.  Sixteen  cents  are  1  dime  and cents. 

8.  Sixteen  inches  are  1  foot  and inches. 

9.  Sixteen  days  are  2  weeks  and days. 

10.  Sixteen  months  are  1  year  and months. 

11.  Sixteen  feet  are  5  yards  and foot. 


61 

i^^^i^  ^^-i^  iViV^ 
lin^-i^  ^^t^  i:xiki^ 

9  stars  and  9  stars  are stars. 

6  and  6  and  6  are 

3+3+3+3+3+3= 
9  twos  are . 

2  times  9  stars  are stars. 

9  times  2  stars  are stars. 

3  times  6  stars  are stars. 

6  times  3  stars  are stars. 

1.  A  butterfly   has   legs.     Two   butterflies 

have legs.     Three  butterflies  have legs. 

2  times  6  legs  are legs. 

3  times  6  legs  are legs. 

2.  On  one  front  foot  and  one  hind  foot  a  cat  has 

toes.     On  both  front  feet  and  both  hind  feet  a 

cat  has toes. 

2  times  9  toes  are toes. 

3.  Six  teaspoons  make  a  set.  In  2  sets  there 
are  teaspoons.  In  3  sets  there  are  tea- 
spoons. 


62 


19  and  3  = 
39  and  3  = 
59  and  3  = 
79  and  3  = 
99  and  3  = 


29  and  3 
49  and  3 
69  and  3 

89  and  3 
98  and  3 


23  less  3  are 
46  less  3  are 
68  less  3  are 
89  less  3  are 
103  less  3  are 


34  less  3  are 
53  less  3  are 
75  less  3  are 
92  less  3  are 
153  less  3  are 


1.  One  half  of  22  =  i  of  24  = 

2.  One  half  of  26  =  i  of  28  = 

3.  One  half  of  42  =  i  of  44  = 

4.  One  half  of  46  =  i  of  48  = 

5.  One  half  of  62  =  i  of  64  = 

6.  One  half  of  66  =  h  of  68  = 

7.  One  half  of  82  =  *  of  84  = 

8.  One  half  of  86  =  I  of  88  = 
Add  by  lO's  to  100;  thus,  10,  20,  30,  40,  etc. 
Add  by  lO's  from  2  to  102:  thus,  2,  12,  22,  etc. 


63 
2 


4  5  (5 

Take  a  4-inch  sqiiare  of  pajier.  Fold  as  suggested  on  page  59.  Cut  off  a 
row  of  1-inch  squares  fi-om  one  side  of  the  paper,  and  a  row  from  one  end  of 
what  remains.  You  will  then  have  a  3-inch  square.  Cut  this  as  indicated 
by  the  heavy  lines  in  the  diagTam  on  this  page ;  then  fold  into  a  box  1  inch 
square  and  1  inch  deep,  making  the  center  square  the  bottom  of  the  box. 
Paste  Xo.  1  upon  Xo.  2,  and  Xo.  3  upon  Xo.  1.  Paste  Xo.  4  upon  Xo.  5,  and 
Xo.  6  upon  Xo.  4.     The  box  will  contain cubic  inch. 

Observe  that  this  box  will  contain  exactly  one  fourth  as  much  as  the  box 
described  on  page  59. 

]\Ieasure  1  cubic  inch  of  sand ;  2  cubic  inches ;  3  cubic  inches ;  4  cubic 
inches. 

To  THE  Teacher. — Provide  a  few  small  boxes  or  bottles  and  require  the 
pupils  to  estimate  in  cubic  inches  the  capacity  of  each.  Then  require  the 
pupils  to  measure  each,  using  sand  and  the  box  described  above. 

P-3 


64 

1.  The  mercuiy  in  the  thermometer  stood  at  68. 
It  went  up  10  degrees.     It  then  stood  at . 

2.  The  mercury  in  the  thermometer  stood  at  74. 
It  went  down  10  degrees.     It  then  stood  at . 

3.  At  one  dime  a  yard,  5  yards  of  ribbon  cost 
cents. 


5  times  10  cents  are cents. 

4.  Hiram  paid  40  cents  for  tickets  to  the  mati- 
nee. The  tickets  cost  10  cents  each.  There  were 
tickets. 

10^  are  contained  in  40^ times. 

5.  Ada  bought  3  ferry  tickets  for  18  cents.  One 
ticket  cost cents. 

One  third  of  18  cents  is cents. 


6.  Seventeen  eggs  are  1  dozen  and . 

7.  Seventeen  cents  are  1  dime  and cents. 

8.  Seventeen  inches  are  1  foot  and inches. 

9.  Seventeen  days  are  2  weeks  and days. 

10.  Eighteen  eggs  are  1  and dozen. 

11.  Eighteen  inches  are  1  and feet. 

12.  Eighteen  days  are  2  weeks  and days. 


10  stars  and  10  stars  are  — —  stars. 

5  and  5  and  5  and  5  = 

4  +  4  +  4  +  4  +  4  = 

5  times    4  stars  are stars. 

4  times    5  stars  are stars. 

2  times  10  stars  are stars. 

10  times    2  stars  are stars. 


2  nickels  are  equal  to dime. 

3  nickels  are  equal  to cents. 

1.  A  horse  needs shoes.     Two  horses  need 

shoes.     Three  horses  need  shoes.     Four 

horses  need shoes.    Five  horses  need shoes. 

2.  The  area  of  an  oblong  4  inches  by  5  inches  is 


square  inches. 

4  times  5  sq.  in.  are 

5  times  4  sq.  in.  are 

Q-l 


sq.  m. 
sq.  in. 


66 

18  and  4  =  28  and  4 

38  and  4  =  48  and  4 

58  and  4  =  68  and  4 

78  and  4  =  88  and  4 


22  less  4  =  32  less  4 

42  less  4  =  52  less  4 

68  less  4  =  78  less  4 

89  less  4  =  97  less  4 

102  less  4  =  152  less  4 


3G  =  30  and  6. 

1.  One  third  of  36  is  (1  ten  and  2)  — . 

39  =  30  and  9. 

2.  One  third  of  39  is  (1  ten  and  3) . 

63  =  60  and  3. 

3.  One  third  of  63  is  (2  tens  and  1) . 

4.  Bessie's  book  cost  39  cents.  Her  sister's  book 
cost  one  third  as  mnch.  Her  sister's  book  cost 
cents. 

Subtract  by  lO's  from  100  to  10. 

Subtract  by  lO's  from  102  to  2. 

Q-2 


67 


Fold  as  suggested  on  page  59.  Cut  off  a  row  of  l-inch  squares  from  one 
side  of  the  paper.  Cut  also  as  indicated  by  the  heavy  lines  in  the  diagram 
on  this  page.     Fold  and  paste  so  as  to  make  a  1-inch  cube. 

Observe  the  number  of  its  corners,  edges,  and  faces.  Each  face  is  what 
kind  of  a  square?  How  many  such  cubes  can  be  put  into  the  box  described 
on  page  59?  How  many  such  cubes  are  necessary  to  build  a  2-inch  cube? 
See  page  47. 


1.  A  cube  lias faces. 

2.  A  cube  lias corners. 

3.  A  cube  lias edges. 

4.  Each  face  of  a  cube  is  a  square. 

Q-3 


68 

1.  The  mercury  in  the  thermometer  stood  at  78. 
It  went  lip  4  degrees.     It  then  stood  at . 

2.  The  mercury  in  the  thermometer  stood  at  92. 
It  went  down  4  degrees.     It  then  stood  at . 

3.  At  20  cents  a  yard,  2  yards  of  lace  cost  — — 

cents. 

2  times  20  cents  are cents. 

4.  Miriam  earns  4  cents  an  hour.     To  earn  20 
cents,  she  must  work hours. 

4  cents  are  contained  in  20  cents  — —  times. 

5.  Belle  paid  20  cents  for  4  tickets.     One  ticket 
cost cents. 

One  fourth  of  20  cents  is cents. 


6.  Nineteen  buttons  are  I  dozen  and . 

7.  Nineteen  cents  are  I  dime  and  — -  cents. 

8.  Nineteen  days  are  2  weeks  and days. 

9.  Nineteen  inches  are  I  foot  and inches. 

10.  Nineteen  months  are  1  year  and months. 

11.  Twenty  buttons  are  1  dozen  and . 

12.  Twenty  inches  are  1  foot  and inches. 

13.  Twenty  months  are  1  year  and months. 

Q-4 


69 

7  and  7  and  7  = 
7  threes  = 

3  times  7  stars  are stars. 

7  times  3  stars  are stars. 

2  3-cent  stamps  cost cents. 

3  3-cent  stamps  cost cents. 

4  3-cent  stamps  cost cents. 

5  3-cent  stamps  cost cents. 

6  3-cent  stamps  cost cents. 

7  3-cent  stamps  cost cents. 

1.  There  are days  in  one  week. 

2.  There  are days  in  two  weeks. 

3.  There  are days  in  three  Aveeks. 

4.  Two  dimes  and cent  equal  21  cents. 

5.  The  area  of  an  oblong  3  inches  by  7  inches  is 
—  square  inches. 

3  times  7  sq.  in.  are sq.  in. 

7  times  3  sq.  in.  are sq.  in. 


70 

17  and  4  =  27  and  4:  = 

37  and  4:=  47  and  4  = 

57  and  4  =  67  and  4  = 

77  and  4  =  87  and  4  = 

97  and  4  =  96  and  4  = 


21  less  4  =  31  less  4 

41  less  4  =  51  less  4 

65  less  4  =  74  less  4 

87  less  4  =  94  less  4 

101  less  4  =  151  less  4 


m  =  60  and  6. 

1.  One  third  of  66  is  (2  tens  and  2)  — 

69  =  60  and  9. 

2.  One  third  of  69  is  (2  tens  and  3)  — 

93  =  90  and  3. 

3.  One  third  of  93  is  (3  tens  and  1)  — 

Add  by  2's  from  2  to  50. 
Snbtract  by  2's  from  50  to  2. 
Add  by  lO's  from  4  to  104. 
Subtract  by  10' s  from  104  to  4. 


71 

Take  an  8-inch  square  of  paper.  Fold  as  directed  on  page  59.  This  will 
make  2-inch  squares  instead  of  1-incli  sciuares.  Cut  as  directed  on  page  07. 
Fold  and  paste  so  as  to  make  a  2-inch  cube. 

Observe  the  number  of  its  corners,  edges,  and  faces.  Each  face  is  what 
kind  of  a  square?  The  area  of  each  face  is  liow  many  square  inches?  Each 
face  is  how  many  times  as  large  as  the  face  of  a  1-inch  cube. 


EEVIEW  PAGE  43. 
Think  of  a  ?>-inch  square. 

1.  The  perimeter  of  a  3-incli  square  is inches. 

4  times  3  inches  are inches. 

2.  The    area    of    a  3-inch    square  is square 

inches. 

3  times  3  sq.  in.  are sq.  in. 


inches. 


Think  of  a  4-inch  square. 

3.  The  perimeter  of  a  4-inch  square  is  - 

4  times  4  inches  are inches. 

4.  Tlie  area  of    a  4-inch  square  is  square 

inches. 

4  times  4  sq.  in.  are S(|.  in. 


5.  Tell  the  perimeter  and  the  area  of  a  2-inch 
square.     Of  a  1-inch  square. 


72 

1.  The  mercury  in  the  thermometer  stood  at  64. 
It  went  up  20  degrees.     It  then  stood  at . 

2.  The  mercury  in  the  thermometer  stood  at  46. 
It  went  down  20  degrees.     It  then  stood  at . 

3.  In  an  orchard  there  were  3  rows  of  trees,  and 
7  trees  in  each  row.     In  all  there  were trees. 

3  times  7  trees  are trees. 

4.  A  lady  divided  18  apples  among  some  boys, 
giving  to  each  boy  3  apples.     There  were boys. 

3  apples  are  contained  in  18  apples times. 

5.  Lilian  divided  a  piece  of  ribbon  20  inches 

long  into  4  equal   pieces.     Each   piece   was  

inches  long. 

One  fourth  of  twenty  inches  is inches. 


6.  Twenty-one  buttons  are  1  dozen  and 

7.  Twenty-one  cents  are  2  dimes  and  - 


8.  Twenty-one  inches  are  1  foot  and inches. 

9.  Twenty-one   months   are    1    year    and    

months. 

10.  Twenty-one  days  are weeks. 

11.  Twenty-one  feet  are  yards. 


73 

8  and  8  and  8  = 

3  times  8  stars  are stars. 

8  times  3  stars  are stars. 

1.  An  ox  needs  shoes.     Three  oxen  need 

shoes. 

3  times  8  shoes  are shoes. 

2.  A  tripod  has  3  legs.     Eight  tripods  have 

legs. 

8  times  3  legis  are lees. 


'b'- 


3.  Three  weeks  and days  are  24  days. 

4.  Two  dimes  and  — -  cents  are  24  cents. 

5.  The  area  of  an  oblong  3  inches  by  8  inches  is 
—  square  inches. 

3  times  8  sq.  in.  are sq.  in. 

8  times  3  sq.  in.  are sq.  in. 

6.  Two  eights  are .  Three  eights  are . 

7.  Two  sevens  are .  Three  sevens  are . 

8.  Two  sixes  are .  Three  sixes  are . 

9.  Two  fives  are .  Three  fives  are . 


74 

17  and  5  =  27  and  5 

37  and  5  =  47  and  5 

57  and  5  =  67  and  5 

77  and  5=  87  and  5 


21  less  5  =  31  less  5 

41  less  5  =  51  less  5 

69  less  5  =  78  less  5 

86  less  5  =  95  less  5 

101  less  5  =  151  less  5 


1.  One  half  of  24  =  i  of  25  is 

2.  One  half  of  26  =  i  of  27  is 

3.  One  half  of  22  =  i  of  23  is 

4.  One  half  of  44  =  h  of  45  is 

5.  One  half  of  46  =  i  of  47  is 

6.  One  half  of  42  =  i  of  43  is 

7.  One  half  of  48  =  i  of  49  is 

i  of  4  inches  =  4  inches  are  i  of 
^  of  5  inches  =  5  inches  are  i  of 
i  of  6  inches  =         6  inches  are  i  of 


75 

Take  a  12-inch  square  of  paper.  Fold  as  directed  on  page  59.  This  will 
divide  the  paper  into  3-inch  squares.  Cut  as  dii'ected  on  page  67.  Fold  and 
paste  so  as  to  make  a  3-inch  cube. 

Observe  the  number  of  its  corners,  edges,  and  faces.  Each  face  is  what 
kind  of  a  square?  The  area  of  each  face  is  how  many  square  inches?  Each 
face  is  how  many  times  as  large  as  the  face  of  a  1-inch  cube? 


TJdnk  of  an  ohlong  2  i7iches  hy  3  inches. 

1.  The  perimeter  of   an  oblong  2  inches   by  3 

inches  is . 

3  in.  +  3  in.  +  2  in.  +  2  in.  = 

2.  The  area  of  an  oblong  2  inches  by  3  inches  is 
square  inches. 

2  times  3  sq.  in.  are sq.  in. 

3  times  2  sq.  in.  are sq.  in. 


Think  of  an  oblong  2  inches  hy  4  inches, 

3.  The   perimeter  of   an  oblong   2  inches  by  4 
inches  is inches. 

4  in.  +  4  in.  +  2  in.  +  2  in.  = 

4.  The  area  of  an  oblong  2  inches  by  4  inches  is 
square  inches. 

2  times  4  sq.  in.  are sq.  in. 

4  times  2  sq.  in.  are sq.  in. 


76 

1.  A  farmer  had  35  slieep  in  one  pen  and  6  in 
another.     In  both  pens  there  were sheep. 

2.  Edwin  drew  a  line  32  inches  long.     He  erased 

6  inches   of   the   line.     What    remained  was  

inches  long. 

3.  An  electric  car  goes  at  the  rate  of  8  miles  an 
hour.     In  three  hours  it  goes miles. 

3  times  8  miles  are miles. 

4.  How  many  2-quart  jars  can  be  filled  from  a 
pail  containing  14  quarts? 

2  quarts  are  contained  in  14  quarts times. 

5.  Mr.  Nelson  paid  48  dollars  for  the  rent  of  a 

house  for  2  months.     This  was  at  the  rate  of 

dollars  a  month. 

One  half  of  48  dollars  is dollars. 


6.  Twenty-two  days  are  3  weeks  and  day. 

7.  Twenty-three  days  are  3  weeks  and days. 

8.  Twenty-four  days  are  3  weeks  and days. 

9;  Twenty-two  cents  are  2  dimes  and cents. 

10.  Twenty-four  cents  are  2  dimes  and  —  cents. 

11.  Twenty-four  feet  are yards. 


77 

i^i^i^  ^^^ 

6  and  6  and  G  and  6  = 

4  times    6  stars  are stars. 

6  times    4  stars  are stars. 

2  times  12  stars  are stars. 

2  dozen  are . 

2  years  are months. 

2  feet  are inches. 

1.  One  and  1  half  feet  are inches. 

2.  One  and  1  half  years  are months. 

3.  One  and  1  half  dozen  are . 

4.  One  and  1  fonrth  feet  are inches. 

5.  One  and  1  fourth  years  are months. 

6.  One  and  1  fourth  dozen  are . 

7.  The  area  of  an  oblong  4  inches  by  6  inches  is 
—  square  inches. 

4  times  6  sq.  in.  are sq.  in. 

6  times  4  sq.  in.  are sq.  in. 


78 


16  and  5  = 
36  and  5  = 
56  and  5  = 
76  and  5  = 


26  and  5 
46  and  5 
66  and  5 
86  and  5 


22  less  5  = 
42  less  5  = 
68  less  5  = 
85  less  5  = 


32  less  5 
52  less  5 
79  less  5 
96  less  5 


64  =  60  and  4. 

1.  One  half  of  64  =  i  of  65  is 

2.  One  half  of  66  =  i  of  67  is 

3.  One  half  of  62  =  i  of  63  is 

84  =  80  and  4. 

4.  One  half  of  84  =  i  of  85  is 

5.  One  half  of  86  =  ^  of  87  is 

6.  One  half  of  82  =  i  of  83  is 


i  of  7  inches  = 
i  of  8  inches  = 
i  of  9  inches  = 


7  inches  are  i  of 

8  inches  are  i  of 

9  inches  are  i  of 


79 

Take  an  8-inch  square  of  paper.  Fold  as  directed  on  page  59.  This  will 
divide  the  paper  into  2-inch  squares.  Cut  as  directed  on  page  63.  Fold  and 
]iaste  so  as  to  make  a  box  2  inches  by  2  inches  by  2  inches. 

Fill  the  box  with  sand,  using  the  box  described  on  page  Go  as  a  measure. 

Observe  that  the  box  will  hold  8  cubic  inches  of  sand;  that  4  cubic  inches 
fill  the  box  "half  fulL" 

Observe  that  the  solid  content  of  the  box  is  the  same  as  the  solid  content 
of  a  2-inch  cube.     See  page  47. 


Think  of  an  ohlon<j  3  incJics  Jtij  4  inclies. 

1.  The   perimeter  of  an  oblong  3  inches  by  4 
inches  is inches. 

4  in.  +  4  in.  +  3  in.  +  3  in.  = 

2.  The  area  of  an  oblong  3  inches  by  4  inches  is 
sqnare  inches. 

3  times  4  sq.  in.  are sq.  in. 

4  times  3  sq.  in.  are sq.  in. 

Think  of  an  ohloncj  2  inches  by  6  inches. 

3.  The  perimeter  of   an   oblong  2   inches  by  6 
inches  is inches. 

6  in.  +  6  in.  +  2  in.  +  2  in.  = 

4.  The  area  of  an  oblong  2  inches  by  6  inches  is 
square  inches. 

2  times  6  sq.  in.  are sq.  in. 

6  times  2  sq.  in.  are sq.  in. 


80 

1.  Marie  paid  35^  for  a  book  and  11^  for  paper. 
For  both  she  paid ^. 

2.  Isaac  had  a  rope  35  feet  long.     He  gave  his 

playmate  11  feet  of  the  rope.     He  then  had  

feet. 

3.  A  train  moves  at  the  rate  of  23  miles  an  hour. 
In  3  hours  it  moves miles. 

3  times  23  miles  are miles. 

4.  A  4-inch  square  contains square  inches. 

A  4-inch  square  is  how  many  times  as  large  as  a 
2-inch  square? 

4  sq.  in.  are  contained  in  16  sq.  in. times. 

5.  Herman  received   24j^   for  working  4   hours. 
This  was  at  the  rate  of cents  per  hour. 

One  fourth  of  24^  is cents. 


6.  Twenty-four    square    inches    are   equal   to   an 
oblong  4  inches  wide  and inches  long. 

7.  Twenty-four   square    inches   are    equal   to  an 
oblong  2  inches  wide  and inches  long. 

8.  Twenty  square  inches  are  equal  to  an  oblong 
2  inches  wide  and inches  long. 


81 

5  times  5  stars  are  stars. 

1.  Five  nickels  are cents. 

2.  Two  dimes  and  5  cents  are cents. 

3.  Two  years  and  2  months  are months. 

4.  Two  feet  and  1  incli  are inches. 

5.  Two  dozen  and  3  are . 

6.  Three  weeks  and  tt  days  are days. 

7.  Eight  yards  and foot  are  25  feet. 

8.  Eight  yards  and  2  feet  are feet. 

9.  Tlie  area  of  a  4-inch  sqnare  is  square 

inches. 

4  times  4  sq.  in.  are sq.  in. 

10.  The  area  of  an  oblong  3  inches  by  4  inches 

is square  inches. 

3  times  4  sq.  in.  are sq.  in. 

4  times  3  sq.  in.  are sq.  in. 


82 

15  and  6  =  25  and  6 

35  and  6  =  45  and  6 

55  and  6  =  65  and  6 

75  and  6  =  85  and  6 

95  and  6  =  94  and  6 


22  less  6  =  32  less  6 

42  less  6  =  52  less  6 

68  less  6  =  79  less  6 

86  less  6  =  97  less  6 

102  less  6  =  152  less  6 


30  =  20  and  10. 

1.  One  half  of  30  =  i  of  32  is 

50  =  40  and  10. 

2.  One  half  of  50  =  h  of  52  is 

70  =  60  and  10. 

3.  One  half  of  70  =  i  of  72  is 

90  =  80  and  10. 

4.  One  half  of  90  =  i  of  92  is 


m. 


i  of  11  inches  =  11  inches  are  i  of  - 

w  of  13  inches  =  13  inches  are  i  of in 

U-2 


83 


1.  Two  pints  arc  1  quart. 

Two  quarts  are pints. 

2.  Three  pints  are quarts. 

Three  quarts  are pints. 

3.  Four  pints  are quarts. 

Four  quarts  are pints 

4.  Five  pints  are quarts. 

Five  quarts  are pints. 

5.  Six  pints  are quarts. 

Six  quarts  are pints. 

6.  Seven  pints  are quarts. 

Seven  quarts  are pints. 

7.  Eight  pints  are quarts. 

Eight  quarts  are pints. 

8.  Nine  pints  are quarts. 

Nine  quarts  are pints. 

9.  Ten  pints  are quarts. 

Ten  quarts  are pints. 

U-3 


84 

1.  Albert  paid  25 f^  for  mittens  and  12^  for  a  tie. 
For  both  he  paid  ■ cents. 

2.  From  a  can  of  milk  containing  27  quarts,  12 

quarts  were  sold.     There  remained  in  the  can 

quarts. 

3.  A  family  used  5  quarts  of  milk  each  day.  In 
5  days  this  family  used quarts. 

5  times  5  quarts  are quarts. 

4.  Augustus  divided  a  piece  of  copper  wire  24 
inches  long  into  pieces  6  inches  long.  There  were 
pieces. 

6  in.  are  contained  in  24  in. times. 

5.  Alfred  divided  a  piece  of  copper  wire  25 
inches  long  into  5  equal  pieces.  Each  piece  was 
inches  long. 

One  fifth  of  25  inches  is inches. 


6.  Twenty-five  days  are  3  weeks  and days. 

7.  Twenty-five  inches  are  2  feet  and inch. 

8.  Twenty-five  months  are  2  years  and mo. 

9.  Twenty-five  eggs  are  2  dozen  and . 

10.  Twenty-five  feet  are  8  yards  and foot. 


85 


i^ik^  ikt^i^  i^in^ 
^i^^  ikiki^  ^i^i^ 
i^i^^  i^^^  -^i^i^ 

3  times  9  stars  are stars. 

9  times  3  stars  are stars. 

1.  Five  nickels  and  2  cents  are cents 

2.  Two  dimes  and  6  cents  are cents. 

3.  Two  feet  and  3  inches  are inches. 

4.  Two  years  and  2  months  are months. 

5.  Two  years  and  3  months  are months. 

6.  Three  weeks  and  3  days  are days. 

7.  Twelve  quarts  and  1  pint  are pints. 

8.  The  area  of  an  oblong  3  inches  by  9  inclies 
is square  inches. 

3  times  9  sq.  in.  are sq.  in. 

9  times  3  sq.  in.  are sq.  in. 

9.  The  area  of  an  oblong  3  inches  by  5  inches 
is square  inches. 

3  times  5  sq.  in.  are sq.  in. 

5  times  3  sq.  in.  are sq.  in. 

10.  The  area  of  an  oblong  3  inches  by  6  inches 
is square  inches. 


86 


17  and  11  = 
37  and  11  = 
57  and  11  = 

77  and  11  = 


27  and  11 
47  and  11 
67  and  11 
87  and  11 


48  less  11  = 

67  less  11  = 

89  less  11  = 

108  less  11  = 


58  less  11 

77  less  11 

99  less  11 

158  less  11 


32  =  20  and  10 

1.  One  half  of  32  = 
One  half  of  36  = 

52  =  40  and  10 

2.  One  half  of  52  = 
One  half  of  56  = 

72  =  60  and  10 

3.  One  half  of  72  = 
One  half  of  76  = 

92  =  80  and  10 

4.  One  half  of  92  = 
One  half  of  96  = 

V-2 


and  2. 

i  of  34  is 

h  of  38  is 

and  2. 

i  of  54  is 

i  of  58  is 

and  2. 
I  of  74  is 

i  of  78  is 

and  2. 

A  of  94  is 
i  of  98  is 


87 


1.  A  3-incli  cube  contains cubic  inches;  that 

is,  it  is times  as  large  as  a  1-inch  cube. 

3  times  3  cubic  inclies  are cubic  inches. 

8  times  9  cubic  inches  are cubic  inches. 

V-3 


1.  A  farmer  had  34  sheep  in  one  pen  and  12  in 
another.     In  both  he  had sheep. 

2.  A  dealer  had  4:6  sheep.  He  sokl  12  of  them. 
He  then  had sheep. 

3.  A  family  used  3  quarts  of  milk  each  day.  In 
1  week  this  family  used quarts. 

7  times  3  quarts  are quarts. 

4.  A  lady  had  a  3-inch  cube  of  maple  sugar.  She 
divided  it  equally  among  her  grandchildren.     Each 

child   received  9   cubic   inches.     There    were  

children. 

9  cu.  in.  are  contained  in  27  cu.  in. times. 

5.  Clyan  divided  a  2-inch  cube  of  maple  sugar 
equally  between  himself  and  Chester.  Each  had 
cubic  inches. 

One  half  of  8  cu.  in.  is cu.  in. 


6.  Twenty-six  inches  are  2  feet  and inches. 

7.  Twenty-six  days  are  3  weeks  and days. 

8.  Twenty-six  months  are  2  years  and mo. 

9.  Twenty-seven  buttons  are  2  dozen  and . 

10.  Twenty-six  (20  and  6)  pints  are quarts. 


89 

^^^^  ^^^ 
^^^^  t^i^i^ 

4  times  7  stars  are stars. 

1.  Two  feet  and  4  inches  are inches. 

2.  Two  dimes  and  6  cents  are cents. 

3.  Two  years  and  4  months  are months. 

4.  Fonr  weeks  are days. 

5.  Fonr  weeks  and  1  day  are  - 

6.  Two  dozen  and  5  eggs  are  ~ 


-  days. 

-  eggs. 

7.  Fom-teen  quarts  (10  and  4)  are pints. 

8.  The  area  of  an  oblong  4  inches  by  7  inches  is 
—  square  inches. 


Two  apples  x  2  =  * 
Three  feet  x  2  = 
Four  chairs  x  2  = 
Five  dimes  x  2  = 

Six  inches  x  2  = 


2  times  2  are 
2  times  3  are 
2  times  4  are 
2  times  5  are 
2  times  6  are 


*  To  be  read,  Two  apples  multiplied  by  2 
w-i 


90 

16  and  12  =  26  and  12  = 

36  and  12  =  46  and  12  = 

56  and  12  =  66  and  12  = 

76  and  12  =  86  and  12  = 

96  and  12  =  90  and  12  = 


27  less  12  =  37  less  12 

47  less  12  =  57  less  12 

68  less  12  =  78  less  12 

89  less  12  =  99  less  12 

107  less  12  =  157  less  12 


iki^  ^t^  ^i^ 

1.  One  third  of  6  stars  is stars. 

Six  stars  are  1  third  of stars. 

2.  One  third  of  9  stars  is stars. 

Nine  stars  are  1  third  of stars. 


3.  Add  by  2's  from  1  to  51;  thus,  1,  3,  5,  etc. 

4.  Subtract  by  2's  from  51  to  1 ;  thus,  51,  49,  etc. 

5.  2  +  2  +  1  +  1  +  2  +  1  +  2  +  2  +  2  +  1  +  2  +  2  = 


91 


1.  From  9  o'clock  until  12  o'clock  it  is hours. 

2.  From  1  o'clock  until  4  o'clock  it  is hours. 

3.  An  hour  is  60  minutes.     Half  an  hour  is 

minutes.     A  quarter  of  an  hour  is minutes. 

4.  From  1  o'clock  until  quarter  past  1  it  is 

minutes. 

5.  From  quarter  past  1  until  quarter  of  2  it  is 
minutes. 


6.  From  20  minutes  past  1  until  20  minutes  of  2 
it  is minutes. 

7.  Look  upon  the  clock  face  and  count  by  o's 
from  0  to  60. 

8.  Where  is  the  long  hand  of  the  clock  at  25 
minutes  past  12?  At  quarter  past  1?  At  half 
past  2  ?     At  quarter  of  3  ? 


92 

1.  If  to  a  rope  24  feet  long  13  feet  be  added,  tlie 
rope  will  then  be feet  long. 

24  ft.  +  13  ft.  = 

2.  If  13  feet  be  cut  off  from  a  rope  36  feet  long, 
the  remainder  will  be feet  long. 

36  ft.  -  13  ft.  = 

3.  Charles  had  a  piece  of  rope  9  feet  long.  Ben- 
jamin had  a  piece  3  times  as  long.  Benjamin's 
rope  was feet  long. 

9  ft.  X  3  = 

4.  Henry  divided  a  piece  of  rope  28  feet  long  into 
pieces  7  feet  long.     There  were pieces. 

28  ft.  ^  7  ft.  = 

5.  James  divided  a  piece  of  rope  21  feet  long  into 
3  equal  pieces.     Each  piece  was feet  long. 

21  ft.  ^  3  = 

6.  Twenty-eight  inches  are  2  feet  and inches. 

7.  Twenty-nine  days  are weeks  and day. 

8.  Twenty-eight  feet  are  9  yards  and foot. 

9.  Twenty-eight  square  inches  are  equal  to  an 
oblong  4  inches  by inches. 

28  sq.  in.  ^  4  sq.  in.  = 


93 


t^^^  ^^^ 
^i^^  ^^^ 

5  times  6  stars  are stars. 

6  times  5  stars  are stars. 

1.  Two  feet  and  6  inches  are inches. 

2.  Two  dimfes  and  9  cents  are cents. 

3.  Two  years  and  6  months  are months. 

4.  Two  dozen  and  5  eggs  are eggs. 


5.  Four  weeks  and  2  days  are 

6.  Nine  yards  and  1  foot  are  - 


-  days, 
feet. 


7.  The  area  of  an  oblong  5  inches  by  6  inches  is 
—  square  inches. 

5  times  6  sq.  in.  are sq.  in. 

6  times  5  sq.  in.  are sq.  in. 

3  times  2  are .  3  times  6  are . 

3  times  3  are .  3  times  7  are . 

3  times  4  are .  3  times  8  are  - — . 

3  times  5  are .  3  times  9  are . 


94 

13  and  13  = '  23  and  13 

33  and  13  =  43  and  13 

53  and  13  =  63  and  13 

73  and  13  =  83  and  13 


28  less  13  =  38  less  13 

48  less  13  =  58  less  13 

69  less  13  =  79  less  13 

87  less  13  =  97  less  13 

108  less  13=  158  less  13 


^^  ^i^  ^^ 

1.  Two  thirds  of  6  stars  are stars. 

i^^->z  ^^^  •  •  • 

2.  Six  stars  are  2  thirds  of stars. 

i^i^^  i^i^-^  i^i^i^V 

3.  Two  thirds  of  9  stars  are stars. 

4.  Four  stars  are  2  thirds  of stars. 

Add  by  3's  from  3  to  51;  thus,  3,  6,  9,  12,  etc. 


95 

1.  Carl  works  from  7  o'clock  in  the  morning  until 
noon;  and  from  1  o'clock  in  the  afternoon  until  6 
o'clock.     Each  day  he  works  —  hours. 

2.  From  5  minutes  of  10  o'clock  to  5  minutes 
after  10  o'clock  it  is minutes. 

3.  From  10  minutes  before  9  o'clock  to  10  min- 
utes after  9  o'clock  it  is minutes. 

4.  David  works  from  8  o'clock  in  the  evening 
until  4  o'clock  in  the  morning.  Each  night  he 
works hours. 

5.  Tell  where  the  hands  of  the  clock  are  at  25 
minutes  past  12;  at  25  minutes  before  1.  From 
25  minutes  past  12  to  25  minutes  before  1  it  is 
minutes. 

6.  From  20  minutes  past  12  to  20  minutes  before 
1  it  is minutes. 

7.  A  train  was  due  at  quarter  past  4.  It  arrived 
at  20  minutes  past  4.     It  was minutes  late. 

8.  A  certain  school  is  in  session  5  hours  each 
day  and  5  days  each  week.  How  many  hours  of 
school  in  each  week?  How  many  hours  of  school 
in  2  weeks?    How  many  hours  of  school  in  3  weeks? 


96 

1.  Willie  left  the  school-room  at  10  minutes  past 

2  and  was  absent  15  minutes.     He  returned  at 

minutes  past  2. 

10  min.  +  15  min.  = 

2.  Harry  left  the  school-room  at  quarter  past  2 

and  returned  at  25  minutes  past  2.     He  was  absent 

minutes. 

25  min.  -  15  min.  = 

3.  Ora  was  tardy  10  minutes.  Samuel  was  tardy 
6  times  as  many  minutes  as  Ora.  Samuel  was 
tardy  — —  minutes,  or  1 . 

10  min.  X  6  = 

4.  A  boy  earned  5  cents  an  hour.  To  earn  30 
cents  he  must  work hours. 

30j^  ^^  = 

5.  A  man  earns  90  cents  in  3  hours.  In  one 
hour  he  earns cents. 

90^  -^  3  = 

6.  Thirty  inches  are  2  feet  and inches. 

7.  Thirty  days  are  4  weeks  and days. 

8.  Thirty  square  inches  are  equal  to  an  oblong  5 
inches  by inches. 

30  sq.  in.  -^  5  sq.  in.  = 


97 


4  times  8  stars  are  — 
8  times  4  stars  are  — 

1.  Two  feet  and  7  inches  are  - 

2.  Four  weeks  and  3  davs  are 


3.  Two  years  and  8  months  are 

4.  Ten  yards  and  1  foot  are 


stars, 
stars. 

-  inches. 

—  days. 
months. 


feet. 


cents. 


5.  Tavo  dozen  and  8  eggs  are  — 

6.  Three  dimes  and  2  cents  are  - 

7.  The  area  of  an  oblong  4  inches  by  8  inches  is 
—  square  inches. 

Two  apples  x  4  =  4  times  2  are 

Three  feet  x  4  =  4  times  3  are 

Four  chairs  x  4  =  4  times  4  are 

Five  dimes  x  4  =  4  times  5  are 

Six  inches  x  4  =  4  times  6  are 

Seven  pints  x  4  =  4  times  7  are 

Eight  years  x  4  =  4  times  8  are 


98 


13  and  20  = 
32  and  20  = 
5Q  and  20  = 
78  and  20  = 

25  ai 
44  a] 
65  a] 

89  a] 

id  20  = 
lid  20  = 
[id  20  = 
Qd20  = 

5SS  20  = 
;ss  20  = 
iss  20  = 
3SS  20  = 

—  stars. 

^^r^       A    A    A    A    i 

27  less  20  = 
44  less  20  = 
63  less  20  = 
81  less  20  = 

36  k 
55  l€ 
78  le 
92  h 

1 

A 

.  Two  thirds  of  12  stars  are  — 

.  Twelve  stars  are  2  thirds  of 

ADD.    • 
bode 

2  4          2           1 

3  12          4 
12           12 
3          3           3           2 
2          2           11 
12           2           3 

2 

a 

2 
2 
1 
2 
2 
1 

4  M     •  •  •  •  • 

stars. 

f           g 
3           2 

1  2 

2  4 

3  2 
2           2 
1           4 

h 
1 

2 
2 
2 

2 
1 

99 


1.  One  gallon  is  4  quarts. 

One  quart  is 

2.  Two  gallons  are quarts. 

Two  quarts  are 

3.  Three  gallons  are quarts. 

Three  quarts  are 

4.  Four  gallons  are quarts. 


of  a  gallon. 
—  of  a  gallon. 
of  a  gallon. 


Four  quarts  are 

5.  Five  gallons  are quarts. 

Five  quarts  are 

6.  Six  gallons  are quarts. 


gallon. 
gallons. 


Six  quarts  are 

7.  Seven  gallons  are quarts. 

Seven  quarts  are 


gallons. 
—  gallons. 


100 

1.  A  dealer  had  24  quarts  of  milk  in  one  can  and 
14  quarts  in  another.     In  both  he  had  — —  quarts. 

24  qt.  +  14  qt.  = 

2.  Mr.  Hill  had  36  quarts  of  milk  in  a  can.  From 
this  he  sold  13  quarts.     There  remained quarts. 

36  qt.  -  13  qt.  = 

3.  A  family  used  a  gallon  of  milk  each  day.  In 
a  week  this  family  used quarts  of  milk. 

4  qt.  X  7  = 

4.  Mr.  Boston  divided  24  quarts  of  milk  among 
some  customers,  giving  to  each  1  gallon.  There 
were customers. 

24  qt.  -  4  qts.  = 

5.  A  farmer  divided  18  quarts  of  milk  equally 
among  3  calves.     Each  calf  had quarts. 

18  qt.  ^  3  = 

6.  Thirty-two  cents  are  3  dimes  and cents. 

7.  Thirty-tAvo  inches  are  2  feet  and inches. 

8.  Thirty-two  square  inches  are  equal  to  an  oblong 
4  inches  by inches. 

9.  Thirty  square  inches  are  equal  to  an  oblong  3 
inches  by inches. 


101 

5  times  7  stars  are stars. 

7  times  5  stars  are stars. 

1.  Two  feet  and  10  inches  are inches. 

2.  Two  feet  and  11  inches  are inches. 

3.  Eight  gallons  and  3  quarts  are quarts. 

4.  Ten  yards  and  4  feet  are feet. 

5.  Two  dozen  and  10  eggs  are eggs. 

6.  Three  dimes  and  5  cents  are cents. 

7.  The  area  of  an  oblong  5  inches  by  7  inches  is 
—  square  inches. 

Two  apples  x  5  =  5  times  2  are  — 

Three  feet  x  5  =  5  times  3  are  — 

Four  chairs  x  5  =  5  times  4  are  — 

Five  dimes  x  5  =  5  times  5  are  — 

Six  inches  x  5  =  5  times  6  are  — 

Seven  pints  x  5  =  5  times  7  are  — 


102 


i5^nd21 

= 

25  and  21  = 

35  and  21 

= 

45  and  21  = 

55  and  21 

= 

65  and  21  = 

75  and  21 

= 

85  { 

md  21  = 

:ess  21  = 

48  less  21 

— 

58  ] 

64  less  21 

= 

75  less  21  = 

87  less  21 

= 

92  less  21  = 

108  less  21 

= 

158] 

less  21  = 

ADD. 

a          b 

C 

d 

e 

f 

24        35 

46 

37 

26 

38 

32         21 

32 

52 

42 

40 

g          h 

i 

J 

k 

1 

25         33 

36 

42 

51 

82 

32         23 

52 

34 

14 

13 

SUBTEACT. 

m          n 

0 

P 

q 

r 

86         47 

58 

65 

72 

84 

21         22 

13 

23 

10 

20 

103 


1.  One  ijeck  is  8  quarts. 

One  quart  is of  a  peck. 

2.  Two  pecks  are quarts. 

Two  quarts  are of  a  peck. 

3.  Three  pecks  are quarts. 

Three  quarts  are of  a  peck, 

4.  Four  pecks  are quarts. 


5.  One  bushel  is  4:  pecks. 

One  peck  is of  a  bushel. 

6.  Two  bushels  are pecks. 

Two  pecks  are of  a  bushel. 

7.  Three  bushels  are pecks. 

Three  pecks  are of  a  bushel. 

8.  Four  bushels  are pecks. 


104 

1.  A  farmer  had  250  sheep.      He   bought  52 
more.     He  then  had sheep. 

250  sheep  +  52  sheep  = 

2.  Arthur  had  |1.50.     He  spent  25  cents.     He 

then  had  . 

11.50  less  25^  = 

3.  Harris  had  |2.10.     His  brother  had  2  times 
as  much  money.     His  brother  had . 

12.10  X  2  = 

4.  A  man  paid  $4.00  for  tickets  that  cost  50^ 
each.     He  bought tickets. 

$4.00  ^  50^  =  4  -^  i  = 

5.  Mr.  Davis  paid  |600  for  3  acres  of  land. 
One  acre  cost dollars. 

1600  ^  3  = 

6.  Thirty-live   quarts   are   8   gallons    and   

quarts. 

7.  Thirty-five  days  are weeks. 

8.  Thirty-five  cents  are  3  dimes  and cents. 

9.  Thirty-five  inches  are  2  feet  and inches. 

10.  Thirty-five    square    inches   are   equal   to   an 

oblong  5  inches  by inches. 

35  sq.  in.  -^  7  sq.  in.  = 


106 


6  times  6  stars  are 

The  area- 
1.  Of  a  3-inch  square  is  - 
•2.   Of  a  4-incli  square  is  - 

3.  Of  a  5-inch  square  is  - 

4.  Of  a  6-inch  square  is  - 


stars. 


The  perimeter- 

5.  Of  a  3-inch  square  is 

6.  Of  a  4-inch  square  is 

7.  Of  a  5-inch  square  is 

8.  Of  a  6-inch  square  is 


square  inches, 
square  inches, 
square  inches, 
square  inches. 


inches, 
inches, 
inches, 
inches. 


6  times  3  are 
6  times  4  are 


6  times  5  are 
6  times  6  are 


106 
ADD. 

a  b  c  d  e  f  g 

25  35  45  55  35  45  55 

25  25  25  25  45  45  15 


h 

i 

J 

k 

1 

m 

n 

34 

34 

44 

54 

74 

64 

74 

26 

36 

26 

16 

SUBTRACT. 

16 

26 

16 

a 

b 

c 

d 

e 

f 

g 

84 

63 

92 

75 

86 

57 

54 

24 

23 

32 

25 

36 

17 

24 

h 

i 

J 

k 

1 

m 

n 

80. 

70 

60 

30 

50 

90 

40 

9 

8 

5 

6 

7 

4 

6 

0 

P 

q 

r 

s 

t 

u 

20 

30 

40 

50 

60 

70 

90 

4 

1 

3 

6 

3 

5 

6 

Two  apples  x  7  =  7  times  2  are 

Three  feet  x  7  =  7  times  3  are 

Four  chairs  x  7  =  7  time^i  4  are 


107 

ADD. 

a             b            c            cl  e  f  g 

25          24          33          28  69  45  34 

0            8            8            4  2  7  8 


h 

i 

J 

k 

1 

m 

n 

63 

46 

34 

42 

55 

74 

66 

7 

6 

8 

9 

SUBTEACT. 

6 

8 

6 

a 

b 

c 

d 

e 

f 

^ 

81 

81 

81 

81 

81 

81 

81 

1 

2 

4 

3 

5 

7 

6 

h 

1 

J 

k 

1 

m 

n 

81 

81 

81 

81 

81 

81 

81 

9 

8 

10 

11 

12 

14 

13 

MULTIPLY. 

a 

b 

C       d 

e 

f 

^ 

22 

32 

43    34 

24 

23 

33 

2 

2 

2     2 

2 

2 

2 

Two  apples  x  8  =  8  times  2  are 

Three  feet  x  8  =  8  times  3  are 

Four  chairs  x  8  =  8  times  4  are 


108 


ADD. 

a 

b 

c 

d 

e 

f 

g 

24 

36 

55 

63 

44 

27 

38 

28 

46 

26 

18 
SUBTRACT. 

48 

25 

24 

a 

b 

c 

d 

e  • 

f 

g 

42 

42 

42 

42 

42 

42 

42 

12 

13 

15 

14 

MULTIPLY. 

16 

17 

18 

a 

b 

c 

d 

e 

f 

g 

25 

35 

45 

25 

15 

15 

26 

2 

2 

2 

3 

3 

4 

2 

r 

rwo 

apples 

X   9: 

= 

9  times  2  are  = 

r 

rhree  feet  x 

:  9  = 

9  times  3  are  = 

DIVIDE.     I. 

t 

a 

b 

c 

2  ft. 

)  12  ft. 

2  ft. )  22  ft. 

2  ft. 

)  48  ft. 

DIVIDE.     II. 

a 

b 

c 

2: 

)  12  ft. 

2  )  22  ft. 

21 

48  ft. 

.11^    H70m) 


5'JS417 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


!!    illii 


iliii 


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